THE  LIBRARY 

OF 

THE  UNIVERSITY 

OF  CALIFORNIA 

RIVERSIDE 

GIFT  OF 


Dr.  Gordon  Watkins 


•sv 


THE   NATURE   OF   CAPITAL  AND   INCOME 


VO 


THE  NATURE   OP  CAPITAL 
AND  INCOME 


BY 
IRVING   FISHER,    PH.D. 

PROFESSOR    OF    POLITICAL    ECONOMY,    YALE    UNIVERSITY 


THE   MACMILLAN   COMPANY 

LONDON:  MACMILLAN  &  CO.,  LTD. 

1906 

All  rights  reserved 


H13601 

F5 


COPYRIGHT,  1906, 
BT  THE  MACMILLAN  COMPANY. 


Set  up  and  electrotyped.     Published  September,  1906. 


Ncrfoonfc 

J.  9.  Cushin?  it  CD.  —  Berwick  &  Smith  Co. 
Norwood,  Mass.,  U.S.A. 


TO 
WILLIAM  GRAHAM  SUMNER 

WHO  FIRST  INSPIRED  ME 

WITH 

A   LOVE  FOR 
ECONOMIC   SCIENCE 


PREFACE 

THIS  book  is  an  attempt  to  put  on  a  rational  foundation 
the  concepts  and  fundamental  theorems  of  capital  and 
income.  It  therefore  forms  a  sort  of  philosophy  of  eco- 
nomic accounting,  and,  it  is  hoped,  may  supply  a  link  long 
missing  between  the  ideas  and  usages  underlying  prac- 
tical business  transactions  and  the  theories  of  abstract 
economics.  To  some  readers  it  may  seem  that  certain 
elementary  topics  have  been  treated  at  undue  length  ;  but, 
as  experience  shows  that  economic  structures  built  on 
hasty  and  inadequate  generalizations  inevitably  collapse, 
it  seems  hardly  possible  to  take  too  much  pains  in  making 
the  foundations  secure.  On  the  other  hand,  topics  which 
are  in  their  nature  technical  or  which  digress  from  the 
main  theme  —  and  in  particular  mathematical  formulae  — 
have  been  relegated  to  appendices. 

Many  of  the  theses  maintained  will  undoubtedly  fail 
to  command  assent  on  a  first  reading,  for  in  any  orderly 
presentation  of  a  subject  it  is  impossible  to  forestall  all 
objections  as  they  occur.  The  aim  has  been  to  pre- 
serve a  definite  sequence  by  which  each  step  prepares 
the  way  for  those  which  follow ;  but  this  plan  has  ne- 
cessitated the  postponement  of  some  topics  beyond  the 
point  at  which  a  consciousness  of  their  difficulties 
might  begin  to  trouble  the  reader.  He  is  therefore 
asked  to  stay  judgment  until  he  has  finished  the  work, 
and,  if  necessary,  to  reread  those  parts  in  which  his  diffi- 
culties were  first  encountered.  This  suggestion  is  espe- 
cially urged  in  regard  to  the  treatment  of  income,  the 
concept  of  which  forms  the  central  theme  of  the  book. 
Many  of  the  friendly  critics  to  whom  the  manuscript  has 


viii  PREFACE 

been  shown  have  at  first  dissented  strongly  from  the  con- 
clusions of  Chapter  VII,  but  have  invariably  withdrawn 
their  objections  after  finishing  Chapter  XIV. 

The  nature  of  income  is  a  subject  which  has  not  hitherto 
received,  in  economic  literature,  the  attention  it  deserves. 
Income  plays  an  important  role  in  all  economic  problems ; 
it  is  income  for  which  capital  exists  ;  it  is  income  for  which 
labor  is  exerted ;  and  it  is  the  distribution  of  income  which 
constitutes  the  disparity  between  rich  and  poor. 

Nor  is  the  subject  of  interest  solely  to  theoretical  econo- 
mists. It  appeals  to  practical  men  of  affairs  and  to  those 
who  are  interested  in  problems  of  social  reform,  as  well  as 
to  the  special  classes  of  accountants,  actuaries,  and  mathe- 
maticians. The  book  is  so  arranged  that  the  general 
reader  may,  if  he  so  desires,  omit  the  technical  .por- 
tions, such  as  the  appendices  and  possibly  Chapter  XVII. 
It  is  suggested  that  all  readers  should  give  special  atten- 
tion to  Chapters  VI,  VII,  IX,  and  XIV. 

The  problem  of  nomenclature  has  proved  not  a  little 
puzzling.  In  general,  each  term  has  been  employed  in 
one,  and  only  one,  sense ;  but  to  follow  this  plan  exclu- 
sively has  not  been  found  practicable.  Several  words  are 
sometimes  used  for  the  same  concept,  —  for  instance,  "re- 
sources" and  "assets,"  or  "utility"  and  "desirability";  and 
sometimes  the  same  word  has  been  used  in  more  than  one 
sense,  as  in  the  case  of  "  capital,"  which  may  mean  capital- 
goods  or  capital-value.  But  special  pains  have  been  taken 
to  avoid  any  confusion  or  uncertainty  of  meaning.  The 
definitions  have  been  carefully  framed,  and  will  be  found 
collected  in  a  glossary  at  the  end. 

A  few  fragments  of  the  book  have  appeared  in  a  some- 
what different  form  in  economic  periodicals,  and  the 
whole  book  may  be  said  to  be  only  the  elaboration  of  the 
ideas  outlined  some  years  ago  in  the  Economic  Journal. 
I  would  express  my  thanks  to  the  publishers  of  the 
Economic  Journal  for  permission  to  use  unaltered  some 


PREFACE  ix 

passages  from  "What  is  Capital?"  1897,  "Senses  of 
Capital,"  1898,  and  "  The  Role  of  Capital  in  Economic 
Theory,"  1898,  and  to  the  Quarterly  Journal  of  Economics 
for  similar  permission  with  reference  to  "  Precedents  for 
Defining  Capital,"  1904. 

I  wish  also  to  express  my  obligations  to  the  many 
persons  who  have  aided  me  in  the  preparation  of  this 
work,  among  them  especially  my  wife ;  my  brother,  Mr. 
Herbert  W.  Fisher;  my  colleagues,  Professor  Henry  C. 
Emery,  Professor  John  P.  Norton,  and  Dr.  Lester  W. 
Zartman;  and  my  friends,  Mr.  Richard  M.  Hurd  and 
Mr.  Orland  S.  Isbell  of  New  York  City. 

IRVING  FISHER. 
NEW  HAVEN,  CONN.,  June,  1906. 


CONTENTS 
FIRST   SUMMARY 

CHAPTERS 

INTRODUCTION.     FUNDAMENTAL   CONCEPTS       .         .  I-III 

PART   I.     CAPITAL IV-VI 

PART   II.     INCOME VII-X 

PART   III.     CAPITAL   AND   INCOME          ....     XI-XVI 
PART   IV.     SUMMARIES  XVII-XVIII 


xii  CONTENTS 


SECOND   SUMMARY 

INTRODUCTION 

CHAPTBE 

PAGE 

I.     WEALTH       ......... 

3 

II.     PROPERTY    ......... 

.       18 

III.     UTILITY        

.       41 

PART   I 

l\T      CAPIT\L       

51 

V.     CAPITAL  ACCOUNTS      ....... 

.       66 

VI.     CAPITAL  SUMMATION  ....... 

.       90 

PART   II 

VII.     INCOME         ......... 

.     101 

VIII.     INCOME  ACCOUNTS       ....... 

.     119 

IX.     INCOME  SUMMATION     ....... 

.     141 

X.     PSYCHIC  INCOME           

.     165 

PART   III 

XL     FOUK  INCOME-CAPITAL  RATIOS    ..... 

.     183 

XII.     CONCEPT  OF  RATE  OF  INTEREST          .... 

.     191 

XIII.     VALUE  OF  CAPITAL     ....... 

.     202 

XIV.     EARNINGS  AND  INCOME         ...... 

.     227 

XV.     CAPITAL  AND  INCOME  ACCOUNTS         .... 

.     256 

XVI.     THE  RISK  ELEMENT    ....... 

.     265 

PART   IV 

XVII.     SUMMARY  OF  PART  III        

.     303 

XVIII.     GENERAL  SUMMARY     ....... 

.     323 

GLOSSARY.     SUMMARY  OF  DEFINITIONS     ..... 

.     329 

APPENDICES  

341 

INDEX 

413 

ANALYTICAL  TABLE  OF  CONTENTS 


CHAPTER   I 
WEALTH 

PAGE 

§  1.  Definition  of  wealth 3 

§  2.  Classification  of  wealth    ........  5 

§  3.  Measurement  of  wealth 8 

§  4.  Price  of  wealth          .........  9 

§  5.  Market-,  asking-,  appraised-price     .        .         .         .        .         .11 

§  6.  Value  of  wealth 13 

§  7.  Quantity,  price,  and  value  contrasted 14 

§  8.  Accuracy  in  measurement  of  quantity,  price,  and  value       .  15 


CHAPTER   II 
PROPERTY 

§  1.  Definition  of  property 18 

§  2.  Definition  of  services 19 

§  3.  Definition  of  rights 20 

§  4.  Wealth  and  property  correlative 22 

§  5.  Table  illustrating  this  correlation     ......  24 

§  6.  A  guide  for  finding  wealth  underlying  given  property  rights  .  24 

§  7.  A  second  guide  :  One  property  right  overlaid  by  another        .  31 

§  8.  A  third  guide  :  Property  rights  are  always  to  existing  wealth  32 

§  9.  Total  ownership  is  aggregate  of  partial  rights  .         .         .         .34 

§  10.  Classification  of  property  rights        ......  36 

§  11.  Importance  of  a  clear  understanding  of  wealth  and  property  .  38 


CHAPTER   III 
UTILITY 

§  1.    Desirability  vs.  satisfaction 41 

§  '2.    Synonyms  for  desirability  (lUility,  etc.)  .....  42 

§  :V    Desirability  vs.  services    ........  43 

xiii 


xiv  ANALYTICAL   TABLE   OF   CONTENTS 

PA«K 

§  4.    Total  and  marginal  desirability 44 

§  5.    Law  of  decreasing  marginal  desirability  .....      46 


CHAPTER   IV 
CAPITAL 

§  1.    Fund  and  flow  distinguished.     Capital  and  income         .         .  51 

§  2.    Discordant  definitions  of  capital       ......  53 

§  3.    Fundamental  truths  in  these  conflicting  definitions          .         .  57 

§  4.    Confusions  resulting  from  neglect  to  introduce  time  element  58 

§  5.   The  weight  of  economic  usage          ......  GO 

§  6.    Popular  and  business  usage 61 

§  7.    Correct  terminology  less  important  than  correct  thinking        .  65 


CHAPTER   V 

CAPITAL  ACCOUNTS 

§  1.  Senses  of  capital       .........  60 

§  2.    Book  capitalization 08 

§  3.  Book  and  market  values  ........  70 

§  4.    Summary  of  senses  of  capital 72 

§  5.  Case  of  decreasing  capital-balance    ......  73 

§  6.  Effect  of  payments  between  stockholders  and  company  .        .  75 

§7.    "  Rights  to  subscribe " 77 

§  8.    Stock  watering 70 

§  9.    Insolvency 81 

§  10.  Pseudo-insolvency    .........  82 

§  11.  Creditor  nominally  takes  no  risk      ......  82 

§  12.    But  practically  creditor  is  risk-taker 84 

§  13.  Winding  up  a  bankrupt  company     ......  80 

§  14.    One  bankruptcy  leads  to  another 87 

§  15.  Summary          ..........  89 


CHAPTER   VI 

CAPITAL  SUMMATION 

§  1.    Methods  of  couples  and  balances     ......       00 

§  2.   Distinction  between  accounts  of  real  and  fictitious  persons      .       02 
§  3.    Summation  by  couples  brings  into  relief  concrete  capital         .       03 


ANALYTICAL   TABLE    OF   CONTEXTS  XV 


PAUK 

§4. 

Nature  of  credit        

96 

§5- 

Importance  of  distinguishing  methods  of  couples  and  balances 

97 

CHAPTER   VII 

INCOME 

§1- 

Difficulties  of  defining  income  ....... 

101 

§  2 

103 

§3. 

The  real-income  concept  ........ 

104 

§4. 

Error  of  including  as  income  both  commodities  and  services  . 

10« 

§5- 

Vain  attempts  to  escape  the  pitfalls  thus  laid  .... 

109 

§6. 

Income  not  restricted  to  "  enjoyable  "  elements 

112 

§7. 

So-called  social  and  individual  income      ..... 

113 

§  8. 

Conclusion        ......... 

115 

CHAPTER   VIII 

INCOME  ACCOUNTS 

§1- 

Introduction      

119 

§2. 

Specimen  income  and  outgo  accounts       ..... 

121 

§3. 

Cost  of  construction  is  to  be  included  in  outgo  accounts  . 

124 

§*• 

Devices  for  making  income  regular  ...... 

127 

§5. 

Applications  of  income  accounting  ...... 

129 

§6. 

Example  of  individual  accounts        ...... 

131 

§7. 

Income  and  outgo  account  for  negative  capital  (liabilities) 

134 

S  8. 

133 

ff    *•*• 

§9. 

Income  accounts  for  fictitious  persons      ..... 

138 

§  10. 

Relation  of  income  accounts  to  capital  accounts 

139 

CHAPTER   IX 

INCOME  SUMMATION 

§1- 

Summation  by  "  method  of  balances  "      

141 

§2. 

"Interactions"         ......... 

143 

§3. 

Interactions  which  change  the  form  of  wealth  (production)     . 

145 

§4. 

Interactions  which  change  the  place  of  wealth  (transportation) 

148 

§5. 

Interactions  which  change  the  ownership  of  wealth  (exchange) 

149 

§6. 

Accounts  illustrative  of  the  first  class  (production) 

152 

§7- 

Results  of  combining  these  accounts         ..... 

15(3 

§  8- 

Methods  of  balances  and  couples  contrasted 

1  57 

§9. 

Accounts  illustrative  of  the  third  class,  for  fictitious  persons   . 

158 

§  10. 

Accounts  illustrative  of  the  third  class,  for  real  persons  . 

162 

§  11- 

Conclusion        .......... 

104 

Xvi  ANALYTICAL  TABLE    OF   CONTENTS 

CHAPTER   X 
PSYCHIC  INCOME 

PAGE 

§  1.    Objective  income  leads  up  to  subjective 165 

§  2.   Illustrative  cases       .........  165 

§  3.    Concept  of  subjective  income    .......  167 

§  4.    Objective  and  subjective  incomes  differ  in  time        .         .         .  169 
§  5.    Objective  and  subjective  incomes  differ  as  to  labor  .         .         .170 
§  6.    Labor  the  only  ultimate  cost  of  production      .         .         .         .173 

§  7.    Objective  and  subjective  income  differ  as  to  pain     .         .         .  175 

Summary ...........  177 

Classification  of  services 178 

CHAPTER   XI 

FOUR    INCOME-CAPITAL    RATIOS 

§1.    Resume  of  previous  chapters 183 

§  2.    Physical-  and  value-productivity,  physical-  and  value-return  .  184 

§  3.    Errors  from  confusing  them     .......  186 

§  4.    How  costs,  past  and  future,  affect  values         ....  188 

CHAPTER   XII 
CONCEPT  OF  RATE  OF  INTEREST 

§1.  The  rate  of  interest  as  a  case  of  "  value-return "      .         .        .  191 

§  2.    Annual,  semi-annual,  quarterly,  and  continuous  reckoning     .  192 

§  '.',.    Hate  of  capitalization  or  reciprocal  of  the  rate  of  interest         .  11)4 

§  4.    The  "  premium  "  and  "  price  "  concepts  of  the  rate  of  interest  194 

§  5.    The  conditions  under  which  they  are  interchangeable      .         .  196 

§  6.    Conditions  under  which  they  are  not  interchangeable      .         .  198 

§  7.    The  rate  of  discount 199 

§  8.    Summary 199 

CHAPTER   XIII 
VALUE  OF  CAPITAL 

§  1.    Capital-value  of  a  single  future  item.     The  "discount  curve"  202 

§  2.    Application  to  valuing  capital,  property,  and  wealth        .         .  204 

§3.    Capital-value  of  a  perpetual  annuity         .....  .:<>•"> 

§4.    Application  to  valuing  capital,  property,  and  wealth        .         .  2i>8 

§  ;">.    Capital-value  of  a  terminable  annuity       .....  200 

§6.    Application  to  valuing  capital,  property,  and  wealth        .         .  210 
§7.    Capital-value  of  a  bond    .         .         .         .         .         .         .         .I'll 

§8.    Capital-value  of  any  income  stream  whatever  .         .         .217 


ANALYTICAL   TABLE   OF   CONTENTS  xvii 


§  9.    Capital-value  when  alternative  income  streams  are  possible     .  221 

§  10.    Capital-value  of  a  group  of  articles  ......  223 

§  11.    General  conclusion 223 

CHAPTER   XIV 
EARNINGS  AND  INCOME 

§  1.    Capital-value  less  than  total  anticipated  income       .        .         .  227 

§  2.    Effect  of  a  change  in  the  rate  of  interest           ....  229 

§  3.    Value-return  may  be  greater  or  less  than  rate  of  interest         .  229 

§  4.    Standard  or  earned  income  vs.  realized  income         .         .         .  231 

§  5.    Increase  of  capital  equals  excess  of  earnings  over  income        .  236 

§  6.    A  depreciation  fund  as  a  means  of  standardizing  income          .  238 

§  7.    Sinking  funds 243 

§  8.    Other  devices  for  making  income  regular          ....  244 

§  9.   The  device  of  keeping  a  large  stock  of  instruments          .         .  246 

§  10.    Savings  are  not  a  part  of  realized  income         ....  247 

§11.    Imaginary  case  of  three  brothers      ......  249 

§  12.    An  '"income"  tax  on  the  three  brothers          ....  250 

§  13.    A  misconceived  income  tax  affects  the  use  of  capital        .         .  253 

§  14.   To  consider  "  savings"  income  confuses  capital  and  income   .  254 

CHAPTER   XV 
CAPITAL  AND  INCOME  ACCOUNTS 

§  1.    Capital  and  income  accounts  when  items  recur  regularly.         .  256 

§  2.    Case  in  which  repairs  occur  at  long  intervals  ....  257 

§  3.    The  same,  when  there  is  a  repair  fund  but  no  repairs  as  yet    .  259 

§  4.    The  same,  when  repairs  actually  occur 261 

§  5.    Extraordinary  increases  or  decreases        .....  263 

§  6.    Conclusion 264 

CHAPTER   XVI 
THE  RISK  ELEMENT 

§  1.    Subjective  nature  of  chance      .......  265 

§  2.    Definition  of  chance 269 

§  3.    Risk  as  applied  to  the  rate  of  interest       .....  271 

§  4.    Same,  in  case  future  income  is  dependent  on  rate  of  interest  .  273 

§  5.    Risk  as  applied  to  immediate  income        .....  275 

§6.    "Riskless,"  "mathematical,"  and  "commercial"  values      .  -76 
§  7.    Capital-value  of  a  risky  bond  .         .         .         .         .         .         .277 

§  8.    Riskless,  mathematical,  and  commercial  rates  of  interest         .  270 

§  9.    Inverse  case,  where  instead  of  risk  of  loss  there  is  chance  of  gain  280 


xviii  ANALYTICAL   TABLE   OF   CONTENTS 

PAGE 

§  10.    The  general  case,  where  both  are  present        .         .         .         .281 

§11.    Difficulties  in  practice 283 

§  12.    Enumeration  of  causes  affecting  capital-value           .         .         .  284 

§  13.    Effect  of  chance  on  the  form  of  the  "  discount  curve  "    .         .  280 

§  14.    Effect  of  chance  on  bookkeeping      ......  287 

§  15.    Five  methods  of  avoiding  risk 288 

§  10.    The  method  of  guaranties 288 

§  17.   The  method  of  safeguards 289 

§  18.    The  method  of  increasing  knowledge 291 

§  19.    The  method  of  insurance          .......  291 

§  20.    Forms  of  insurance 294 

§  21.    Shifting  risks  to  speculators.    Dangers  of  imitative  speculations  295 

§  22.   Buying  and  selling  futures 298 

CHAPTER   XVII 
SUMMARY  OF  PART  III  BY  MEANS  OF  DIAGRAMS 

§  1.    Mode  of  representation  adopted        ......  303 

§  2.    Capital-value  as  discounted  income  ......  304 

§  3.    Capital-value  as  mean  between  past  cost  and  future  income    .  305 

§  4.    How  to  combine  capital  curves         ......  309 

§  5.    Resultant  in  case  of  interactions       .         .         .         .         .         .311 

§  6.    Application  to  summation  of  capital  of  individuals  .         .         .314 

§  7.    Application  to  summation  of  capital  of  society         .         .         .  310 

§  8.    An  "interaction"  as  preparatory  to  enjoyable  services  .         .  317 

§  9.    The  risk  element 320 

CHAPTER   XVIII 

GENERAL  SUMMARY 

§  1.    Picture  of  capital  and  income 

§  2.    Summation  of  capital  and  income     ..... 

§  3.    Subjective  counterparts  of  objective  capital  and  income  .        .  3i"> 
§  4.    Relative  changes  in  values  of  capital  and  income     .         .         .327 

§  5.    Final  summary 328 

GLOSSARY 

SUMMARY  OF  DEFINITIONS           ........  329 


APPENDICES 


APPENDIX  TO  CHAPTER  I 

PAGE 

§  1  (to  Ch.  I,  §  7).     Dimensions  of  quantity,  value,  and  price  of 

wealth 341 

APPENDIX  TO  CHAPTER  III 

§  1  (to  Ch.  Ill,  §  4).  Mathematical  expression  for  marginal  desir- 
ability  344 

APPENDIX  TO  CHAPTER  VII 
§  1  (to  Ch.  VII,  §  1).     Specimens  of  current  definitions  of  income  .     345 

APPENDIX  TO  CHAPTER  XI 

§  1  (to  Ch.  XI,  §  2).     Mathematical  dimensions  of  income-capital 

ratios  ............     357 

APPENDIX  TO  CHAPTER  XII 

§  1  (to  Ch.  XII,  §  2).  Mathematical  relations  between  rates  of 
interest  reckoned  annually,  semi-annually,  etc.,  when  the  rates 
are  conceived  in  the  "  price  "  sense 357 

§  2  (to  Ch.  XII,  §  4).  The  same,  when  the  interest  rates  are  con- 
ceived in  the  "  premium  "  sense.  Diagrammatic  representation. 
Economic  interpretation  of  e  .  .  .  .  .  .  358 

§  3  (to  Ch.  XII,  §  6).  A  premium  rate  of  4  per  cent  in  one  year  and 
3  per  cent  thereafter,  means  a  price  rate  of  3.03  per  cent  the 
first  year  and  3  per  cent  thereafter 362 

§  4  (to  Ch.  XII,  §  6).  A  price  rate  of  4  per  cent  in  one  year  and 
3  per  cent  thereafter  means  a  premium  rate  of  37|  per  cent  the 
first  year  and  3  per  cent  thereafter 362 

§  5  (to  Ch.  XII,  §  6).     Mathematical  relations  between  the  rates  of 

interest  as  a  premium  and  as  a  price 363 

§  6  (to  Ch.  XII,  §  7).     Mathematical  relations  between  the  rates  of 

interest  and  discount 364 

§  7  (to  Ch.  XII,  §  7).  Mathematical  relations  between  rates  of  dis- 
count for  different  time  reckonings 366 

§  8  (to  Ch.  XII,  §  8).     Dimensions  of  rates  of  interest,  discount, 

and  capitalization ,  367 

xix 


XX  ANALYTICAL   TABLE   OF   CONTENTS 

APPENDIX  TO  CHAPTER  XIII 

PAGE 

§  1  (to  Ch.  XIII,  §  1).     Formula  for  capital-value  of  a  sum  due  in 

one  year 368 

§  2  (to  Ch.  XIII,  §  1).     Formula  for  capital-value  of  a  sum  F,  due 

at  end  of  any  time  t 368 

§  3  (to  Ch.  XIII,  §  3).     Formula  for  capital-value  of  a  perpetual 

annuity        ...........     369 

§  4  (to  Ch.  XIII,  §  3) .  Formulae  and  diagrams  for  capital-value  of 
annuities  payable  annually,  semi-auuually,  quarterly,  and  con- 
tinuously   369 

§  5  (to  Ch.  XIII,  §  3).     Diagrams  for  discontinuous  and  continu- 
ous income  ...........     371 

§  6  (to  Ch.  XIII,  §  5).     Formula  for  capital-value  of  a  terminable 

annuity        ...........     374 

§  7  (to  Ch.  XIII,   §  5).     Discussion   of   formulas   for   terminable 

annuities  by  diagrams.  "Total  discount."  " Total  interest "  374 
§  8  (to  Ch.  XIII,  §  7).  Formulae  for  value  of  bond  .  .  .378 
§  9  (to  Ch.  XIII,  §  7).  Alternative  method  for  computing  value 

of  a  bond 380 

§  10  (to  Ch.  XIII,  §  7).     Formula  for  a  bond  when  interest  is 

reckoned  oftener  than  yearly 382 

§  11  (to  Ch.  XIII,  §  8).     Formula  for  capital-value  of  any  series  of 

income  installments     .........     382 

§  12  (to  Ch.  XIII,  §  8).     Diagram  and  formula  for  deriving  capital- 
value  from  a  given  continuous  income  stream     ....     383 

§  13    (to   Ch.    XIII,    §   8).      Diagram    showing    the   accumulated 

"amount"  of  a  given  income  stream       .....     .'387 

§  14  (to  Ch.  XIII,  §  10).     Effect  of  reckoning  semi-annually,  quar- 
terly, and  continuously,  on  the  rate  of  interest  realized  from 
the  income  of  a  continuously  replenished  stock  of  articles  .         .     388 
§  15  (to  Ch.   XIII,   §  11).     Influence  of  variation  in  the  rate  of 

interest 390 

§  16  (to  Ch.  XIII,  §  11).     Representation  of  capital  and  income  by 

polar  coordinates         .........     393 


APPENDIX  TO  CHAPTER  XIV 

§  1  (to  Ch.  XIV,  §  5).  When  the  interest  rate  varies,  there  are 
two  rival  concepts  of  "  standard  income  " 396 

§  2  (to  Ch.  XIV,  §  12).  Effect  of  foreknown  tax  on  increa.se  of 

capital 398 

§  3  (to  Ch.  XIV,  §  13).  Unrestricted  application  of  a  true  income 
tax  impracticable 400 


ANALYTICAL   TABLE   OF   CONTENTS  xxi 

APPENDIX  TO  CHAPTER  XVI 

PAGE 

§  1  (to  Ch.  XVI,  §  6).     Mathematical  coefficients  of  probability, 

caution,  and  risk          .........     403 

§  2  (to  Ch.  XVI,  §  7).  Formula  for  mathematical  value  of  a  risky 

bond 403 

§  3  (to  Ch.  XVI,  §  10).  Variability  about  a  mean,  as  measured 

by  the  "  standard  deviation  "      .......     40G 

§  4  (to  Ch.  XVI,  §  20).  Method  of  computing  a  pure  level  life 

insurance  premium     .         .         .        .         .        .        .         .         .410 

INDEX  413 


INTRODUCTION.     FUNDAMENTAL  CONCEPTS 

CHAPTER     I.     WEALTH 
CHAPTER    II.     PROPERTY 
CHAPTER  III.     UTILITY 


THE  NATURE  OF  CAPITAL  AND  INCOME 

CHAPTER  I 

WEALTH 
§    1 

THE  term  "  wealth"  is  used  in  this  book  to  signify  material 
objects  owned  by  human  beings.  According  to  this  defini- 
tion, an  object,  to  be  wealth,  must  conform  to  only  two 
conditions :  it  must  be  material,  and  it  must  be  owned.  To 
these,  some  writers  add  a  third  condition,  namely,  that  it 
must  be  useful.  But  while  utility  is  undoubtedly  an  essen- 
tial attribute  of  wealth,  it  is  not  a  distinctive  one,  being 
implied  in  the  attribute  of  appropriation ;  hence  it  is  redun- 
dant in  a  definition.  Other  writers,  like  Cannan,  while 
specifying  that  an  object,  to  be  wealth,  must  be  useful, 
do  not  specify  that  it  must  be  owned.  They  therefore 
define  wealth  as  "  useful  material  objects."  This  definition, 
however,  includes  too  much.  Rain,  wind,  clouds,  the 
Gulf  Stream,  the  heavenly  bodies  —  especially  the  sun, 
from  which  we  derive  most  of  our  light,  heat,  and  energy 
—  are  all  useful,  but  are  not  appropriated,  and  so  are  not 
wealth  as  commonly  understood.  Still  other  writers 
insist  that  an  article,  to  be  wealth,  must  be  "exchangeable." 
But  this  restriction  would  exclude  parks,  Houses  of  Par- 
liament, the  Hague  Temple  of  Peace,  and  much  other 
trusteed  wealth;  all  wealth,  in  fact,  which  happens  to  fall 
into  permanent  hands.  Although  it  is  essential  that  wealth 
should  be  owned,  it  is  not  essential  that  it  should  contin- 

3 


4  NATURE   OF    CAPITAL   AND   INCOME  [CHAP.  I 

ually  change  owners.  Again,  many  writers,  like  McLeocl, 
omit  the  qualifier  "material"  altogether,  in  order  to 
make  room  for  the  inclusion  of  such  "immaterial  wealth" 
as  stocks,  bonds,  and  other  property  rights,  and  for  human 
and  other  services.  Property  and  services  are,  it  is  true, 
inseparable  from  wealth,  and  wealth  from  them,  but  they 
are  not  wealth.  To  embrace  all  these  under  one  term 
involves  a  species  of  triple  counting.  A  railway,  a  railway 
share,  and  a  railway  trip  are  not  three  separate  items  of 
wealth;  they  are  respectively  wealth,  a  title  to  that 
wealth,  and  a  service  of  that  wealth.  Finally,  a  few  econo- 
mists, like  Tuttle,  have  endeavored  to  break  away  from 
concrete  objects  entirely.  The  term  "  wealth,"  they  main- 
tain, applies,  not  to  the  concrete  objects,  but  to  the  value 
of  these  objects.  Much  may  be  said  in  support  of  this 
contention.  But  as  the  question  is  chiefly  verbal,  that  is, 
not  a  question  of  finding  a  suitable  concept,  but  of  finding 
a  suitable  word  for  a  concept,  it  does  not  seem  advisable 
to  depart  from  the  prevailing  usage  among  economists. 

Wealth,  then,  includes  all  those  parts  of  the  material 
universe  which  have  been  appropriated  to  the  uses  of 
mankind.  It  does  not  include  the  sun,  moon,  or  stars, 
because  no  man  owns  them.  It  is  confined  to  this  little 
planet,  and  only  to  parts  of  that ;  namely,  the  appropriated 
portions  of  the  earth's  surface  and  the  appropriated  objects 
upon  it.  The  appropriation  need  not  be  complete; 
it  is  often  only  partial  and  for  a  particular  purpose, 
as  in  the  case  of  the  Newfoundland  Banks,  which  are  appro- 
priated only  in  the  sense  that  the  fishermen  of  certain 
nations  have  the  right  to  take  fish  in  their  vicinity,  while 
their  waters  are  open  to  all  men  for  all  other  purposes. 
In  fact,  it  is  doubtful  if  there  are  any  objects  owned  so 
unrestrictedly  that  the  owner  of  them  may  use  them  in 
absolute  defiance  of  the  wishes  of  others.  By  appropriation 
of  any  object  is  therefore  meant  that  degree  of  appropria- 
tion to  which  the  object  is  subjected. 


SEC.  2]  WEALTH  5 

Any  single  object  of  wealth  is  called  an  article  of  wealth, 
an  item  of  wealth,  or  an  instrument.  The  term  "instru- 
ment" is  perhaps  the  most  convenient.  It  appears  to 
have  been  first  employed  by  John  Rae  in  1834.1 

§  2 

Various  classes  of  wealth  may  be  distinguished.  Wealth 
which  consists  of  the  earth's  surface  is  called  land;  any 
fixed  structures  upon  it,  land  improvements;  and  the  two 
together,  constituting  immovable  wealth,  real  estate. 
All  wealth  which  is  movable  (except  man  himself)  we 
shall  call  commodities.  A  third  group  includes  human  beings 
-  not  only  slaves  who  are  owned  by  other  human 
beings,  but  also  freemen  who  are  their  own  masters. 

It  is  true  that  freemen  are  not  ordinarily  counted  as 
wealth;  and,  indeed,  they  are  a  very  peculiar  form  of 
wealth,  for  various  reasons :  first,  because  they  are  not, 
like  ordinary  wealth,  bought  and  sold;  secondly,  because 
the  owner  usually  estimates  his  own  importance  so  much 
more  highly  than  any  one  else ;  and  finally,  because  the 
owner  and  the  thing  owned  in  this  case  coincide.  Yet 
they  are,  like  other  wealth,  "material"  and  "owned." 
These  attributes,  and  others  which  depend  on  them,  justify 2 
the  inclusion  of  man  as  wealth.  But  in  order  to  concede  as 
much  as  possible  to  popular  usage,  the  following  supple- 
mentary definition  is  framed :  By  wealth  (in  its  more 
restricted  sense)  we  mean  material  objects  owned  by  man  and 
external  to  the  owner.  This  definition  obviously  includes 
slaves,  but  not  freemen.  But  it  is  more  difficult  of  appli- 
cation than  the  wider  definition  first  given,  as  it  requires 

1  New  Principles  of  Political  Economy,  recently  reprinted  under  the 
title  Sociological  Theory  of  Capital,  Macmillan,  1905. 

2  Among  those  writers  who  have  included  man  in  the  category  of 
wealth  are  Davenant,  Petty,  Canard,  Say,  McCulloch,  Roscher,  Witt- 
stein,  Walras,  Engel,  Weiss,  Dargun,  Ofner,  Nicholson,  and  Pareto. 


6  NATURE    OF    CAPITAL   AND    INCOME  [CHAP.  I 

us  to  separate  into  arbitrary  classes  those  persons  who  are 
intermediate  between  freemen  and  slaves,  such  as  vassals, 
indentured  servants,  long-time  apprentices,  and  negroes  held 
in  peonage.  A  man  bound  out  to  service  for  thirty  years 
is  almost  indistinguishable  from  a  slave,  and  if  the  term  of 
service  be  long  enough  and  the  control  absolute  enough, 
the  distinction  becomes  a  distinction  without  a  difference. 
On  the  other  hand,  the  shorter  the  term  of  service,  the 
nearer  does  his  condition  approach  freedom.  As  a  matter 
of  fact,  most  workers  in  modern  society  are  "hired,"  i.e. 
bound  by  contract  to  some  extent  and  for  some  period  of 
time,  even  though  it  be  for  no  more  than  an  hour,  and  to 
that  extent  are  not  free.  In  short,  there  are  many  degrees 
of  freedom  and  many  degrees  of  slavery,  with  no  fixed 
line  of  demarcation. 

Two  concepts  have  been  defined  which  may  be  des- 
ignated as  "wealth  in  its  more  general  sense  "  and  " wealth 
in  its  more  restricted  sense."  There  need  be  no  confusion 
between  them.  Ordinarily,  when  the  simple  term  "  wealth  " 
is  used,  the  former  concept  will  be  understood,  and  any 
propositions  which  hold  true  of  this  broader  concept  will 
necessarily  apply  also  to  the  narrower  one.  If  we  have  oc- 
casion at  any  time  to  refer  to  the  latter  exclusively,  we  may 
always  make  use  of  the  full  phrase,  "wealth  in  its  more 
restricted  sense." 

There  are  many  admissible  ways  of  classifying  wealth, 
one  being  more  or  less  desirable  than  another  ac- 
cording to  the  purpose  for  which  it  is  intended.  The 
scheme  on  page  7  is  not  based  on  any  one  logical  cri- 
terion, but  is  intended  merely  to  give  the  principal  groups 
into  which  wealth,  as  it  actually  exists,  naturally  falls. 
It  scarcely  needs  to  be  stated  that  the  various  classes  are 
not  always  absolutely  distinct.  Like  all  classes  of  concrete 
things,  they  merge  imperceptibly  from  one  into  another. 
For  this  reason  the  classification  is  of  little  importance 


SEC.  2] 


WEALTH 


except  to  give  a  bird's-eye  view  of  economic  science. 
In  fact,  the  classification  of  concrete  things  is  seldom  of 
paramount  importance  in  scientific  study.  Not  classifica- 
tion, but  analysis,  solves  scientific  problems.1 


land 


productive  land 


ways  of  transit 


I  building  land 


'  crop  land 
grazing  land 
timber  land 
mining  land 
hunting  land 
fisheries 

railways 
roadways 
waterways 
parks 


.  land  improvements 


buildings 
improvements  on 

highways 
I  minor 


overhead 
underground 
surfacing 
bridging 


f  mineral 
'  raw  materials    -{  agricultural 

{ manufactured 

f  by  being  burned 

'  consumable    -i  by  being  eaten  or  drunk 
[  by  being  otherwise  used 

finished  f  mechanical  devices 

products    I  animals 

"hard  money" 
.  durable    \  clothing  and  jewelry 

furniture  and  works  of  art 
reading  matter 
I  minor 
/  slaves 
I  free 


1  See  the  writer's  "What  is  Capital?"  Economic  Journal,  Decem- 
ber, 1896,  p.  516;  and  "Precedents  for  Defining  Capital,"  Quarterly 
Journal  of  Economics,  March,  1904. 


8  NATURE    OF    CAPITAL    AND    INCOME  [CHAP.  I 

§   3 

In  the  definition  of  wealth  were  included  two  attributes : 
wealth  is  material;  and,  it  is  owned.  These  attributes, 
materiality  and  appropriation,  need  to  be  considered  sepa- 
rately. The  remainder  of  this  chapter  will  be  devoted  to 
the  former. 

An  important  and  useful  result  of  the  materiality  of 
wealth  is  that  it  provides  a  basis  for  the  physical  measure- 
ment of  wealth.  Wealth  is  of  many  kinds,  and  each  kind 
is  measured  in  its  own  proper  physical  unit.  These  units 
have  been  handed  down  to  us  from  various  sources  and  in 
great  diversity,  but  all  of  them  are  in  the  last  analysis 
arbitrary. 

Many  kinds  of  wealth  are  measured  by  weight-units. 
This  is  true  of  coal,  iron,  beef,  and  in  fact,  of  most 
"commodities."  Each  unit  consists  of  the  weight  of 
some  particular  piece  of  matter  which  is  adopted  for  con- 
venience as  a  standard.  For  instance,  the  English  pound  is 
simply  a  lump  of  platinum  kept  in  London  and  called  ar- 
bitrarily the  pound. 

Many  articles  are  not  so  conveniently  measured  by 
weight-units  as  by  space-units,  whether  of  volume,  area,  or 
length.  Thus  we  have,  for  volume,  milk  measured  by  the 
quart,  wheat  by  the  bushel,  wood  by  the  cord,  an;!  gas  by 
the  cubic  foot ;  for  areas,  we  have  lumber  sold  by  the  square 
foot  and  land  by  the  acre;  for  length,  we  have  rope,  wire, 
ribbons,  and  cloth  measured  in  feet  and  yards.  All  these 
units  of  length,  area,  and  volume  are  also  quite  arbitrary 
or  conventional.  The  definition  of  the  English  yard,  for 
instance,  is  an  imaginary  line  drawn  between  two  small 
dots  on  gold  plugs  in  a  particular  brass  rod  in  London. 

Many  articles  exist  in  more  or  less  definite  units  which 
need  only  to  be  counted,  as  for  instance,  eggs  or  oranges, 
which  are  measured  by  the  dozen.  Similarly,  writing  paper 
is  reckoned  by  the  quire;  pencils  and  screws  by  the  gross. 


SEC.  3]  WEALTH  9 

In  such  cases  we  say  that  the  article  is  measured 
by  number.  But  "number"  is  by  no  means  peculiar  to  the 
last-named  case.  All  measurement  implies  both  an  ab- 
stract number,  and  a  concrete  unit,  as  "ten  screws,"  "six 
eggs,"  or  "four  pounds-of-granulated-sugar." 

The  last  example  suggests  that  in  order  to  specify  fully 
the  unit  of  any  kind  of  wealth,  it  is  necessary  to  enumerate 
its  particular  attributes,  or  enough  of  them  to  distinguish 
it  from  other  sorts  of  wealth  with  which  it  may  become  con- 
fused. Thus,  it  is  often  necessary  to  specify  what  "grade" 
or  "brand"  is  meant,  as  "Grade  A,"  "Eagle  Brand," 
"  Lackawanna  "  coal.  Sometimes  the  special  sort  is  denoted 
by  a  trade  mark  or  hallmark.  It  is  in  this  way  that  the 
attributes  of  particular  kinds  of  wealth  enter  into  the  con- 
sideration of  economic  science,  and  not,  as  some  have  er- 
roneously supposed,  separately  as  an  "immaterial"  sort  of 
wealth.  The  "fertility"  of  land  is  not  to  be  counted  as 
wealth  apart  from  the  land  itself;  it  is  the  " fertile  land " 
which  is  wealth.  The  "skill"  of  a  mechanic  is  not  wrealth 
in  addition  to  the  man  himself;  it  is  the  "skilled  me- 
chanic" who  should  be  put  in  the  category  of  wealth. 

Of  course,  the  number  expressing  the  measure  of  wealth 
may  be  unity,  as  for  instance,  "one  dwelling."  Sometimes 
there  is  only  one  article  of  the  particular  kind  in  existence. 
There  is  but  one  Battery  Park,  one  Buckingham  Palace, 
one  Koh-i-noor  diamond,  one  Rhynd  papyrus.  Dealers 
call  such  articles  "uniques."  Strictly  speaking,  every  ar- 
ticle might  be  called  a  unique,  even  as  no  two  grains  of 
wheat  are  precisely  alike;  but  for  practical  purposes  we 
overlook  minor  differences  and  regard  articles  sufficiently 
similar  as  homogeneous. 

§  -4 

Thus  each  individual  kind  of  wealth  may  be  measured  in 
its  own  special  unit,  —  pounds,  gallons,  yards ;  but  for  most 
purposes  it  is  more  important  to  measure  the  value  of  wealth, 


10  NATURE    OF    CAPITAL   AND    INCOME  [CHAP.  I 

and  this  may  be  done  in  dollars  and  cents,  pounds  and  shil- 
lings, francs  and  centimes,  and  so  forth.  This  is  also  a  spe- 
cies of  physical  measurement,  but  involves  the  principle  of 
exchange.  So  much  mystery  has  surrounded  the  term 
"value"  that  we  cannot  be  too  careful  to  obtain  correct 
and  simple  ideas  on  the  subject.  In  the  explanation  which 
follows,  the  concept  of  value  is  made  to  depend  on  that 
of  price;  that  of  price  in  turn  on  exchange;  and  finally, 
that  of  exchange  on  transfer. 

An  article  of  wealth  is  said  to  be  transferred  when  it 
changes  owners.  It  is  to  be  observed  that  such  a  change 
does  not  necessarily  imply  any  change  of  place.  Ordinarily, 
the  transfer  of  an  article  involves  change  in  its  posi- 
tion. The  purchase  of  tea  or  sugar  is  accompanied  by 
the  delivery  of  these  articles  across  the  counter  from  dealer 
to  customer.  But  in  many  cases  such  a  change  of  position 
does  not  occur,  and  in  the  case  of  real  estate  it  is  even  im- 
possible. This  distinction  between  change  of  ownership 
and  change  of  position  is  not  always  borne  in  mind.  It  is 
sometimes  said,  for  instance,  that  exports  and  imports 
must  balance  in  a  certain  manner.  But  if  by  "exports" 
we  mean  articles  that  are  sent  out  of  the  country,  and  by 
"imports"  those  which  come  into  it,  the  proposition  will 
not  hold  true.  When,  some  years  ago,  Englishmen  were 
buying  American  breweries,  these  articles,  of  course, 
were  not  exported,  though  they  were  transferred  to  foreign 
ownership. 

Transfers  may  be  voluntary  or  involuntary.  Examples 
of  involuntary  transfers  of  wealth  are  transfers  effected 
either  (1)  through  force  and  fraud  of  individuals,  as  in  rob- 
bery, burglary,  embezzlement,  etc. ;  or  (2)  through  force 
of  government,  as  in  taxes,  court  fines,  etc.  But  at  present 
we  have  to  do  with  voluntary  transfers. 

Voluntary  transfers  are  of  two  kinds:  (1)  one-sided  trans- 
fers, i.e.  gifts  and  bequests;  and  (2)  reciprocal  transfers  or  ex- 
changes, which  are  the  most  important  for  economic  science. 


SEC.  5]  WEALTH  11 

Exchange  of  wealth,  then,  means  the  mutual  and  volun- 
tary transfer  of  wealth  between  two  owners,  each  transfer  being 
in  consideration  of  the  other.  If  either  of  the  two  quanti- 
ties of  wealth  exchanged  is  divided  by  the  other,  the 
quotient  is  called  the  price  of  the  latter.  Thus,  when  three 
bushels  of  wheat  are  traded  for  two  dollars  of  gold,  the 
price  of  the  wheat  is  §  of  a  dollar  per  bushel,  and  the  price 
of  the  gold  is  H  bushels  of  wheat  per  dollar.  In  modern 
times,  one  of  the  two  articles  is  usually  money,  but  this 
condition  is  not  essential,  and  in  primitive  times  was  not 
even  common.  When  the  exchange  is  one  of  money  for 
other  wealth,  it  is  called  a  purchase  (with  reference  to  the 
one  who  parts  with  the  money)  and  a  sale  (with  reference 
to  the  person  who  receives  the  money). 


§  5 

In  order  that  there  may  be  a  price,  it  is  not  necessary 
that  the  exchange  in  question  should  actually  take  place. 
It  may  be  only  a  contemplated  exchange.  A  real  estate 
agent  often  has  an  "asking  price,"  that  is,  a  price  at  which 
he  tries  to  sell,  usually  above  the  price  of  an  actual  sale. 
In  the  same  way  there  is  often  a  "bidding  price/'  which  is 
usually  below  the  price  of  actual  sale.  The  price  of  sale 
thus  generally  lies  between  the  prices  first  bid  and  asked. 
But  it  sometimes  happens  that  the  bidder  refuses  to  raise 
his  bid  and  the  seller  refuses  to  lower  his  asking  price. 
In  such  a  case  no  sale  takes  place  and  the  only  prices  are 
those  bid  and  asked.  Trade  journals  report,  for  many 
commodities,  the  price  of  sale  if  there  is  a  sale,  otherwise 
the  two  prices  bid  and  asked,  or  if  both  do  not  exist,  the  one 
which  does. 

When  there  is  no  sale,  and  especially  when  there  is  no 
price  bid  or  asked,  it  is  not  so  easy  to  answer  the  question, 
What  is  the  price?  Recourse  is  then  had  to  an  "appraise- 
ment" or  appraisal,  which  is  simply  a  more  or  less  skilful 


12  NATURE    OF    CAPITAL    AND    INCOME  [CHAP.  I 

guess  as  to  what  price  the  article  would  or  should  fetch. 
Appraising  or  guessing  at  prices  is  often  very  difficult  in 
practice.  It  is  necessarily  employed,  however,  by  the  gov- 
ernment in  assessing  taxes  and  customs  and  condemning 
land ;  by  insurance  companies  in  settling  claims  and  adjust- 
ing losses ;  by  merchants  in  making  up  inventories  and  other 
statements;  and  by  statisticians  and  others.  In  fact, 
some  people  make  a  living  by  simply  appraising  wealth  on 
which,  for  one  purpose  or  another,  a  price  of  some  sort  must 
be  set.  Evidently,  the  purpose  makes  a  great  difference  in 
the  appraisal.  Sometimes  we  need  to  know  the  price  for 
which  an  article  could  be  sold  at  an  immediate  forced  sale ; 
sometimes,  what  it  might  be  expected  to  bring  if  a  reason- 
able time  were  allowed ;  sometimes,  what  the  owner  would 
probably  take;  sometimes,  what  a  possible  purchaser 
would  probably  give.  These  appraised  prices  may  all  be 
different.  A  family  portrait  may  be  worth  an  untold 
amount  to  the  owner,  but  might  bring  next  to  nothing  if 
actually  sold.  The  owner  would  endeavor  to  appraise  it  at 
a  high  figure  if  he  wished  to  insure  it  against  fire;  but  if 
he  wished  to  borrow  money  on  it,  the  appraisement  would 
doubtless  be  small,  for  the  pawnbroker  would  consider  it 
almost  worthless. 

Thus,  in  practically  making  an  appraisement  we  encoun- 
ter many  difficulties,  owing  partly  to  the  unknown  char- 
acter and  condition  of  the  parties  involved,  and  partly 
to  the  variety  of  interests  to  be  served  by  the  appraisal. 
But  whatever  the  difficulties  and  ambiguities  in  as- 
certaining a  price  or  prices  for  any  article,  the  price  or 
prices  do  actually  exist  without  ambiguity.  The  vague- 
ness comes  wholly  from  failure  to  specify  sufficiently  the 
conditions  under  which  the  exchange  is  to  take  place.  If 
we  specify  in  sufficient  detail  the  conditions  of  the  contem- 
plated exchange,  its  terms  will  be  quite  definite;  but  whether 
or  not  we  can  guess  at  those  terms  correctly  is  quite  another 
matter. 


SEC.  G]  WEALTH  13 

§   6 

Having  obtained  the  price  of  any  kind  of  wealth,  we  may 
compute  the  value  of  any  given  quantity  of  that  wealth, 
without  necessarily  supposing  that  particular  quantity  to 
be  exchanged.  The  value  of  a  given  quantity  of  wealth  is 
found  by  multiplying  the  quantity  by  the  price.  Thus,  if 
the  price  of  wheat  is  §  of  a  dollar  per  bushel,  then  a  lot 
consisting  of  3000  bushels  would  have  a  value  of  3000  x 
$f  per  bushel  or  $2000.  In  other  words,  the  value  of  a 
certain  amount  of  one  kind  of  wealth  is  the  quantity  of 
some  other  kind  for  which  it  would  be  exchanged,  if  the 
whole  amount  were  exchanged  at  the  price  set  upon  it. 
The  exchange  which  sets  the  price  need  not  be  the  ex- 
change of  the  particular  3000  bushels  which  we  are  valuing ; 
some  other  exchange  of,  say,  300  bushels  for  $200  may  set 
the  price.  This  is  one  reason  why  it  is  preferable  to  ex- 
plain price  first  and  value  afterward. 

The  definition  of  value  which  has  been  given,  applying, 
as  it  does,  to  an  aggregate  of  wealth  instead  of  the  unit, 
departs  somewhat  from  economic  usage;  but  it  follows 
closely  the  usage  of  business  men  and  practical  statisti- 
cians. Economists  have  not  usually  thought  it  necessary 
to  distinguish  between  the  purchasing  power  of  the  unit 
and  the  aggregate,  but  have  employed  the  term  "value" 
indiscriminately  to  both.  In  other  respects  also  their  usage 
has  been  somewhat  different  from  that  here  employed. 
Some  of  them  have  confined  "price"  to  a  money  expression, 
i.e.  to  what  is  here  called  money  price,  and  applied  the  term 
"value"  to  purchasing  power  in  "goods."  Others  have 
used  the  term  "price"  in  the  sense  of  what  an  article  ac- 
tually sells  for  (market  price)  and  "value"  in  the  sense  of 
what  it  ought  to  sell  for  (appraised  price  or  reasonable  price). 
Others,  in  turn,  have  used  the  term  "price "in  the  sense  em- 
ployed in  this  book,  but  "value"  in  the  sense  of  the  degree 
of  esteem  in  which  an  article  is  held  ("marginal  utility" 


14 


NATURE    OF    CAPITAL    AND    INCOME 


[CHAP.  I 


or  "subjective  value").  It  seems  preferable  to  conform 
our  definitions  of  value  and  price  as  closely  as  possible  to 
business  usage,  which  instinctively  and  consistently  applies 
the  term  "  price"  to  the  unit  and  "  value "  to  the  aggregate. 

§7 

The  distinction  between  quantity,  price,  and  value  of 
wealth  may  be  seen  clearly  in  any  "inventory,"  such  as  the 
following :  - 


QUANTITY 

PRICE  1  1,- 
WHEAT 

VALL'E   IN 

WHEAT 

Shoes     

1000  pair 

4J  bu.  per  pair 

4,250  bu. 

Beef       
Dwelling  House  . 
Wheat   

300  Ibs. 
1  house 
100  bu. 

5  bu.  per  Ib. 
10,000  bu.  per  house 
1  bu.  per  bu. 

60  bu. 
10,000  bu. 
100  bu. 

14,410  bu. 

In  the  first  column  are  recorded  various  quantities 
of  wealth,  measured  each  in  its  own  special  unit ;  in  the  sec- 
ond column  are  the  prices  of  these  in  wheat ;  while  in  the 
last  column  are  their  values,  also  in  terms  of  wheat.  The 
first  and  last  columns  represent  two  different  modes  of  meas- 
uring wealth.  Statistics  of  wealth,  such  as  those  published 
monthly  by  the  Department  of  Commerce,  usually  give 
both  "quantities"  and  "values."  To  translate  from  one 
to  the  other  we  need  always  a  price  as  go-between. 

It  is  important  not  to  confuse  the  three  columns  with 
each  other.  The  quantity  of  beef  is  a  totally  different  thing 
from  its  value,  and  each  of  these  is  different  from  its  price. 
The  quantity  is  measured  in  pounds  of  beef,  its  value  in 
bushels  of  wheat,  and  its  price  in  bushels  per  pound.  These 
three  magnitudes  are  all  of  different  "dimensions."  Both 
quantity  and  value  are  simply  physical  magnitudes. 
"Value"  as  here  explained  is  not  a  subjective  magnitude 


SEC.  7]  WEALTH  15 

in  the  mind  of  man,  but  purely  objective,  as  money  value, 
or  wheat  value.  It  has,  of  course,  subjective  causes,  but 
these  do  not  concern  us  yet.1 

The  measurement  of  wealth  in  "value"  has  this  great 
advantage  over  its  measurement  in  "quantity,"  that  it 
translates  the  many  kinds  of  wealth  into  a  single  kind. 
All  the  items  in  the  third  column  of  the  inventory  are  thus 
expressed  in  a  common  unit,  the  bushel.  We  may  conse- 
quently add  together  this  column  and  obtain  a  single  sum, 
namely,  14,410  bushels;  but  summation  of  the  first  column 
is  impossible,  because  shoes,  pounds  of  beef,  houses,  and 
bushels  of  wheat  are  incommensurable.  We  see  here  one 
of  the  important  functions  of  money ;  it  brings  uniformity 
of  measurement  out  of  diversity. 

But,  although  this  reduction  to  a  common  measure  is 
practically  convenient,  it  would,  of  course,  be  a  great  mis- 
take to  suppose  that  it  gives  what  may  be  called  "the  true 
measure  of  wealth."  "The  value  of  wealth"  is  an  incom- 
plete phrase;  to  be  definite  we  should  say,  "the  value  of 
wealth  in  terms  of  gold,"  or  in  terms  of  some  other  particu- 
lar article.  We  cannot,  therefore,  use  such  values  for 
comparing  different  groups  of  wealth  except  under  certain 
conditions  and  to  a  limited  degree.  To  compare  the 
wealth-values  of  America  and  England,  of  Ancient  Rome  and 
Modern  Italy,  of  Carnegie  and  Croesus,  will  give  different 
results  according  to  the  standard  of  value  employed. 


We  have  seen  how  to  measure  the  three  magnitudes, — 
quantity,  price,  and  value  of  wealth.  This  measurement 
is,  practical^,  a  very  inaccurate  affair.  The  degree  of  ac- 
curacy attained  is  exaggerated  in  the  minds  of  most  per- 
sons, even  including  business  men.  In  measurements  of 
quantities  of  wealth  there  are  two  sources  of  error,  for  every 

1  Further  explanation  as  to  the  dimensions  of  the  quantity,  price, 
and  value  of  wealth  are  given  in  the  Appendix  to  Chap.  I,  §  1. 


16  NATURE    OF    CAPITAL   AND    INCOME  [CHAP.  I 

measurement  includes,  as  we  have  seen,  two  elements: 
a  unit  of  measure,  which  may  be  inaccurate ;  and  a  number 
or  ratio  between  the  quantity  to  be  measured  and  the  unit, 
which  number  may  also  be  inaccurate.  In  modern  times 
the  first  source  of  error  is  practically  eliminated.  Our 
units  of  weight  and  measure  are  standardized  by  law,  and 
a  pound  weight  in  California  is  equal  to  one  in  Connecticut, 
within  one  part  in  many  thousand.  The  chief  source  of 
error,  therefore,  lies  not  in  the  unit,  but  in  the  ratio  of  the 
wealth  to  that  unit.  In  retail  trade  the  inaccuracy  is  as 
great  as  five  per  cent,  or  greater.  Wholesale  transactions 
are  more  accurate.  A  large  manufacturing  concern  of 
Syracuse  had  its  measurement  of  the  weight  of  caustic 
soda  sold  in  carload  lots  compared  with  the  measurement 
made  by  its  customers,  and  the  results  agreed  within  one 
fifth  of  one  per  cent  on  two  fifty-carload  lots.  Probably 
the  greatest  degree  of  accuracy  ever  obtained  in  com- 
mercial measurements  is  on  the  Mint  scales  used  by  the 
United  States  in  Philadelphia  and  San  Francisco.  These 
scales  weigh  accurately  to  within  about  one  part  in  ten 
million. 

When  we  proceed  from  quantities  of  wealth  to  values, 
we  introduce  still  a  third  source  of  inaccuracy,  namely,  in 
the  price  factor  by  which  we  multiply.  This  is  especially 
true  if  the  price  be  merely  an  "appraised  "  price.  The  price 
of  any  actual  sale  is  an  absolute  fact  and  cannot  be  said  to 
have  any  inaccuracy;  but  the  price  at  which  we  estimate 
that  a  thing  would  sell  under  certain  conditions  is  always 
uncertain.  In  the  case  of  staple  articles,  i.e.  articles  regu- 
larly on  the  market,  a  dealer  can  often  appraise  correctly 
within  one  per  cent.  Real  estate  in  certain  parts  of  a  city 
where  sales  are  active  can  sometimes  be  appraised  correctly 
within  five  or  ten  per  cent;  but  in  the  "dead"  or  out-of- 
the-way  parts  of  some  towns,  where  sales  are  infrequent,  the 
appraisement  becomes  merely  a  rough  guess.  Again,  in 
the  country  districts,  while  farms  in  the  settled  parts  of 


SEC.  8]  WEALTH  17 

Iowa  and  Texas  can  be  appraised  within  ten  or  fifteen  per 
cent,  in  the  backward  parts  even  an  expert's  valuation  is 
often  proved  wrong  by  more  than  fifty  per  cent.  In  some 
cases,  in  fact,  where  a  sale  of  the  article  is  scarcely  conceiv- 
able, an  appraisement  is  almost  out  of  the  question.  To 
estimate  the  value  of  the  Yellowstone  Park  is  impossible, 
unless  we  allow  ourselves  a  range  of  several  hundred  per 
cent.  Similar  wide  limits  must  be  allowed  when  we  try 
to  value  free  human  beings.  We  can  often  give  a  lower 
limit,  but  seldom  an  upper  one.  The  estimates  may  vary 
enormously  with  the  point  of  view.  It  is  sometimes  said, 
"If  I  could  buy  Mr.  So-and-So  at  my  valuation  and  sell 
him  at  his,  I'd  get  rich."  It  would  be  wrong,  however,  to 
conclude,  as  some  writers  have,  that  because  we  cannot 
value  them  accurately,  public  parks  or  freemen  cannot  be 
called  wealth.  When  the  slaves  in  the  South  became  free- 
men they  ceased  to  be  appraised  as  wealth.  The  result 
has  been  somewhat  confusing  to  our  census  statistics. 
The  Manufacturers'  Record  of  Baltimore  recently  issued 
figures  showing  a  sharp  drop  in  the  assessed  valuations  of 
wealth  in  the  South  after  the  war,  and  the  inference  was 
drawn  that  wealth  had  immensely  decreased.  But  a  large 
part  of  this  so-called  decrease  consisted  merely  in  the  change 
of  ownership  of  slaves  from  their  old  masters  to  themselves, 
and  the  consequent  omission  of  them  from  the  statistics. 

Various  writers,  from  Petty  down  to  Engel  and  Nichol- 
son, have  tried  to  assess  the  value  of  human  beings. 
Professor  Nicholson  estimates  roughly  that  the  English 
nation  is  worth  at  least  five  times  the  value  of  other  ex- 
isting wealth  in  England.1  Such  calculations  are  of  course 
of  more  theoretical  than  practical  moment.  They  are  also 
necessarily  inaccurate,  and  involve  in  each  case  some  par- 
ticular supposition  as  to  the  purpose  of  the  appraisement  ; 
for  instance,  whether  it  is  to  indicate  the  earning  power  of 
the  population,  their  value  to  themselves,  or  to  others. 

1  Economic  Journal,  March,  1891,  p.  95. 
c 


CHAPTER  II 

PROPERTY 


THE  definition  of  Wealth  in  the  previous  chapter  restricts 
its  meaning  to  concrete  material  objects.  But  economics 
has  also  to  deal  with  abstract  services,  utilities,  and  property 
rights.  These,  like  material  wealth,  are  bought  and  sold, 
and  are,  in  fact,  often  regarded  as  a  sort  of  "immaterial" 
or  "  incorporeal "  wealth.  It  is,  however,  needless  as  well  as 
confusing  to  include  these  elements  under  the  general  cate- 
gory of  wealth.  They  are  not  wealth,  though  they  are 
intimately  related  to  wealth.  The  definition  given  shows 
that  wealth  has  two  attributes:  it  must  be  material,  and 
it  must  be  owned.  Its  materiality  was  the  subject  of  the 
previous  chapter;  its  ownership  will  be  the  subject  of  the 
present  chapter. 

But  what  is  meant  by  owning  wealth?  We  answer: 
to  have  the  right  to  use  it.  Such  a  right  is  called  prop- 
erty, or,  more  explicitly,  a  property  right.  To  own  a  loaf  of 
bread,  or  to  have  property  or  proprietorship  in  it,  means 
nothing  more  nor  less  than  to  have  the  right  to  eat  it,  or  sell 
it,  or  otherwise  employ  it  to  satisfy  one's  desires.  To  own 
a  suit  of  clothes  is  to  have  the  exclusive  right  to  wear  it. 
To  own  a  carriage  is  to  have  the  right  to  drive  in  it  or 
otherwise  .utilize  it  as  long  as  it  lasts.  To  own  a  plot 
of  land  means  to  have  the  right  to  its  use  forever.  The  con- 
cept of  property  —  the  "right  to  use  wealth"  -is  more 
fully  expressed  by  the  phrase,  the  "right  to  the  uses  of 
wealth."  In  this  phrase  we  have  to  deal  with  two  new 
ideas  —  rights  and  uses  —  each  of  which  needs  to  be  treated 
separately. 

18 


SEC.  2]  PROPERTY  19 


We  need  first  to  understand  what  is  the  nature  of  the  uses 
or  services  of  wealth.  The  services  of  an  instrument  of 
wealth  are  the  desirable  changes  effected  (or  the  undesir- 
able changes  prevented)  by  means  of  that  instrument.  For 
instance,  the  services  of  a  loom  consist  in  changing  yarn  into 
cloth,  or  what  is  called  weaving.  Similarly,  a  plow  per- 
forms the  service  of  changing  the  soil  in  a  particular  manner ; 
a  bricklayer,  of  changing  the  position  of  bricks.  A  dam 
or  dike  performs  the  service  of  preventing  the  water  from 
overflowing  the  land;  a  fence,  of  preventing  cattle  from 
roaming;  a  necklace,  of  sparkling  or  reflecting  light,  and 
thereby  satisfying  the  love  of  beauty  or  the  vanity  of  the 
owner. 

When  services  are  described  as  desirable  events,  it  is 
meant  that  they  are  desired  or  esteemed  by  the  owner  or 
owners,  not  necessarily  by  every  one,  or  even  any  one,  else. 
It  may  even  happen  that  the  events  are  distinctly  distaste- 
ful to  others.  A  factory  whistle  may  be  a  nuisance  to  every 
one  except  the  factory  owner. 

In  this  connection  it  is  important  to  distinguish  between 
the  uses  or  desirable  events,  and  the  utility  or  desirability 
of  those  events.  The  desirable  service  is  a  thing;  it  is 
usually  objective.  The  desirability  of  the  service,  on  the 
other  hand,  is  a  quality,  and  is  purely  subjective.  It  is 
a  feeling  toward  the  events,  not  the  events  themselves. 
In  the  present  chapter  we  do  not  have  to  deal  with  the  de- 
sirability, and  it  will  form  the  subject  of  the  next  chapter. 

Each  sort  of  service  is  measured  in  its  own  appropriate 
unit.  Sometimes  the  measurement  is  by  number,  i.e. 
obtained  by  simply  counting  the  acts  in  wrhich  the  specified 
service  consists,  as,  for  instance,  in  the  case  of  the  strokes 
of  a  printing  press;  sometimes  the  measurement  is  by  time, 
as  in  the  case  of  the  day  laborer;  while  sometimes  the 
measurement  of  the  services  is  expressed  in  terms  of  the 


20  NATURE    OF   CAPITAL    AND   INCOME  [CHAP.  II 

units  of  wealth  affected  by  those  services,  as  in  the  case  of 
so-called  piecework.  The  services  of  a  miner  are  meas- 
ured by  reference  to  the  quantity  of  coal  mined  ;  the  serv- 
ices of  a  planter,  by  the  number  of  acres  planted  ;  and  of  a 
spinning  machine,  by  the  number  of  yards  spun.  Services, 
like  wealth,  are  subject  to  exchange  and,  in  consequence, 
have  prices.  The  quantity  of  any  service  multiplied  by  its 
price  gives  its  value.  When  reduced  to  value  in  a  common 
standard,  all  varieties  of  services  become  commensurable 
with  each  other  and  with  wealth. 

The  opposite  of  a  service  is  a  disservice,  which  is  an  un- 
desirable change  effected  (or  a  desirable  change  prevented) 
by  means  of  wealth.  For  instance,  a  locomotive  renders 
disservices  by  consuming  coal;  a  farm,  by  requiring  fer- 
tilizers and  labor  ;  a  factory,  by  requiring  costs  of  work- 
ing. Disservices,  like  services,  are  measured  in  quantity 
by  special  units  and  made  commensurable  in  value  by 
reduction  to  a  common  standard. 


Having  seen  what  is  meant  by  services  of  wealth,  we  next 
ask  what  is  meant  by  the  right  to  those  services.  "  Right" 
is  a  term  of  jurisprudence,  and  brings  economics  into  con- 
tact with  the  whole  subject  of  legal  and  custom-sanctioned 
relations;  but,  for  our  present  purpose,  it  is  not  necessary 
to  go  far  in  this  direction.  The  right  of  a  person  to  the 
uses  of  an  article  of  wealth  may  be  defined  as  his  liberty, 
under  the  sanction  of  law  and  society,  to  enjoy  the  services 
of  that  article. 

Lawyers  distinguish  between  property  rights  and  per- 
sonal rights;  but,  to  the  economist,  all  rights  are  proprie- 
tary. The  distinction  between  property  and  personal 
rights  exists  only  so  long  as  we  restrict  the  meaning  of 
wealth  to  the  narrower  of  its  two  definitions,  that  is,  only  so 
long  as  we  exclude  free  human  beings.  Here  we  have  an 
instance  in  which  logical  convenience  is  served  by  adopting 


SEC.  3]  PROPERTY  21 

the  broader  definition  of  wealth,  which  includes  human 
beings  even  when  free,  and  by  adopting  also  a  coextensively 
broad  definition  of  property  so  as  to  include  all  rights  known 
to  jurisprudence.  This  being  premised,  it  follows  that 
every  right  is  a  property  right.  No  rights  have  ever  been 
suggested  which  are  not  rights  to  obtain  and  enjoy  the 
uses  of  wealth,  either  persons  or  things.  Even  the  "right 
to  life,  liberty,  and  the  pursuit  of  happiness"  is  simply 
one's  right  to  certain  uses  of  his  own  person.  The  rights 
of  a  husband  over  his  wife  and  of  a  wife  over  her  husband, 
and  the  reciprocal  rights  between  parents  and  children,  as 
well  as  all  other  rights  in  personam,  are  claims  against  par- 
ticular persons;  while  the  right  to  reputation,  to  the  free 
exercise  of  one's  calling,  to  immunity  from  boycott,  perse- 
cution, etc.,  are  claims  upon  the  community  generally.1 
These  rights  are  not  ordinarily  called  property  rights,  just 
as  persons  are  not  ordinarily  called  wealth,  and  for  a  similar 
reason,  —  they  do  not  enter  into  trade.  When  wives 
were  bought  and  sold  they  were  regarded  as  wealth,  and 
marital  rights  as  property.  To-day,  both  are  taken  out  of 
commerce  and  therefore  removed  from  commercial  ideas 
and  terms.  The  economist  need  not,  perhaps,  absolutely 
insist  on  restoring  them;  like  the  business  man,  he  is  chiefly 
interested  in  what  is  salable.  But  in  framing  his  defini- 
tions he  finds  it  difficult,  if  not  impossible,  to  confine  the 
terms  "wealth"  and  "property"  to  objects  which  are  ex- 
changeable, without  thereby  sacrificing  simplicity  and  logi- 
cal convenience,  and  excluding  certain  objects,  such  as  public 
parks  and  former  English  entails,  which,  though  never  sold, 
even  business  men  would  call  wealth  and  property  respec- 
tively. We  therefore  choose  in  this  book  to  frame  our  defi- 
nitions so  as  to  include  such  elements,  even  though  they  be 
not  further  referred  to.  In  definitions,  it  is  usually  better 
to  include  too  much  rather  than  too  little,  and  in  this  case, 

1  Cf.  T.  E.  Holland,  Jurisprudence,  Macmillan,  1S9S,  pp.  50,  80,  87, 

90,  128. 


22  NATURE    OF   CAPITAL   AND   INCOME  [CHAP.  JI 

at  least,  the  superfluous  which  is  included  will  seldom  con- 
cern and  never  embarrass  us. 

Property  rights,  then,  consist  of  rights  to  the  uses  or 
services  of  wealth.  But  the  services  which  we  own  are  al- 
ways and  necessarily  future  services;  the  past  have  per- 
ished. Moreover,  since  all  future  events  are  uncertain,  we 
are  always  constrained  to  reckon  with  the  element  of  chance. 
A  strictly  complete  definition  of  a  property  right,  therefore, 
would  read  as  follows :  A  property  right  is  the  right  to  the 
chance  of  obtaining  some  or  all  of  the  future  services  of  one 
or  more  articles  of  wealth. 

Property  is  measurable,  just  as  are  wealth  and  services, 
each  in  its  own  particular  unit.  Usually  the  measurement 
is  "by  number,"  that  is,  by  counting  the  number  of  rights 
of  the  same  kind.  Thus,  one  hundred  shares  of  preferred 
stock  in  a  particular  company  is  a  statement  of  the  amount 
of  that  particular  property.  The  concepts  transfer,  ex- 
change, price,  and  value  apply  to  property  as  to  wealth  and 
to  services.  Indeed,  as  an  exchange  of  wealth  is  but  a  con- 
cealed exchange  of  services,  so  an  exchange  of  services  is  but 
a  concealed  exchange  of  the  right  thereto,  namely,  prop- 
erty. Hence  the  exchange  of  property  is  the  final  form 
of  exchange,  and  includes  in  itself  all  other  forms  whatso- 
ever. 

§4 

Wealth  and  property,  then,  are  correlative  terms. 
Wealth  is  the  concrete  thing  owned;  property  is  the  ab- 
stract right  of  ownership.  The  two  concepts  mutually 
imply  each  other.  There  can  be  no  wealth  without  prop- 
erty rights  applying  to  it,  nor  property  rights  without  wealth 
to  which  they  apply.  In  fact,  the  proposition  that 
property  and  wealth  are  coextensive  follows  neces- 
sarily from  the  definitions  of  wealth  and  property 
which  we  have  adopted.  But  it  may  readily  be  objected 
that  in  the  actual  concrete  world,  for  which  these  defini- 
tions were  designed,  the  correspondence  between  what  are 


SEC.  4]  PROPERTY  23 

known  as  wealth  and  property  does  not  hold  true.  A  thor- 
ough examination  of  the  case,  however,  will  remove  this 
objection. 

Sometimes  wealth  and  property  rights  are  so  closely 
associated  as  to  be  confused  with  each  other,  so  that,  un- 
less one  stops  to  consider  the  matter,  the  existence  of  the 
two  separate  concepts  would  not  be  suspected.  This  is 
true  in  the  case  of  "fee  simple,"  where  a  piece  of 
land  is  spoken  of  as  a  "piece  of  property."  For  prac- 
tical purposes,  little  objection  can  be  raised  to  such  popular 
usage,  but  even  in  such  cases  strict  accuracy  requires  that 
the  two  ideas  should  be  distinguished.  The  distinction  is 
more  easily  remembered  if  we  employ  the  full  phrase  "prop- 
erty right."  A  loaf  of  bread  is  concrete  wealth,  not  a  prop- 
erty right;  the  right  to  eat  it  is  the  property.  On  the 
other  hand,  in  the  more  involved  cases  of  property  rights, 
we  encounter  the  opposite  difficulty.  The  danger  here  is  in 
separating  the  concepts  of  wealth  and  property  too  far, 
so  as  to  consider  them  as  independent  instead  of  interde- 
pendent. When  railway  shares  are  sold  in  Wall  Street,  the 
investor  is  prone  to  think  of  those  shares  as  entirely  de- 
tached from  any  concrete  wealth.  It  is  unlikely  that  he 
has  ever  seen  or  ever  will  see  the  steel  rails,  cars,  and  loco- 
motives upon  which  those  shares  are  based;  and  indeed, 
the  only  concrete  object  of  which  he  is  likely  to  be  dis- 
tinctly conscious  is  the  paper  certificate  itself.  But  it 
is  clear  that  this  paper  certificate  is  not  itself  the  prop- 
erty, but  merely  the  written  evidence  of  it  and  that  the 
railway  shares,  to  be  property,  involve  a  real  railway 
(wealth)  underneath. 

That  all  wealth  involves  a  property  right  is  not  likely 
to  be  denied  by  any  one;  and  that  all  property  rights  in- 
volve underlying  wealth  should  be  equally  evident.  But 
this  is  not  the  case.  In  fact,  some  of  the  most  dangerous 
fallacies  which  beset  the  business  wrorld,  including  many  of 
the  sophisms  of  credit,  are  due  to  the  difficulty  of  recog- 


24  NATURE    OF   CAPITAL   AND   INCOME  [CHAr.  II 

nizing  the  wealth  lying  behind  property  in  some  of  its  sub- 
limated forms. 

§5 

In  order  not  to  devote  too  much  space  to  this  subject 
the  best  procedure  will  be  to  give  types  of  the  chief  forms 
of  property,  and  to  specify  in  each  case  what  wealth  under- 
lies the  right.  This  is  done  in  the  table  on  pages  26  and 
27,  which  also  specifies  the  services  involved,  and  (where  they 
exist)  the  certificate  or  written  evidence  of  the  property 
right. 

§6 

Probably  ninety  per  cent  of  the  actual  property  in  the 
United  States  would  be  included  under  the  cases  entitled 
Fee  Simple,  Partnership  Rights,  Stocks,  Bonds,  Notes,  and 
Lease  Rights.  In  all  of  these  cases,  the  existence  of  the 
real  wealth  behind  them  is  well  known  and  acknowledged. 
For  practical  purposes,  therefore,  the  proposition  that 
wealth  and  property  are  coextensive  is  already  established. 

Of  the  remaining  cases  some  seem  a  little  obscure  at 
first,  but  they  may  be  readily  solved  if  we  bear  in  mind  a 
few  general  principles : 

The  first  thought  which  should  guide  us  is  that,  given 
any  particular  property  right,  we  should  first  discover  the 
benefits  or  "services"  secured  by  that  right,  then  the  phys- 
ical means  by  which  those  services  are  obtained.  These 
means  are  not  always  identical  with  the  "cause"  of  those 
services.  For  instance,  real  estate  with  a  southern  ex- 
posure is  especially  desired  because  of  the  sunlight  which 
falls  upon  it.  The  sun  may  be  called  the  cause  of  the  sun- 
light, but  the  land  is  the  practical  means  of  obtaining  it. 
To  own  or  not  to  own  the  land  is  to  obtain  or  not  to 
obtain  the  sunlight  which  goes  with  it.  It  is  the  land  which 
puts  the  sunlight  at  the  disposal  of  its  owner.  On  the  other 
hand,  when  a  lamp  gives  its  light  it  is  not  only  means,  but 
also  cause. 


SEC.  0]  PROPERTY  25 

Following  this  idea,  that  wealth  is  simply  the  means 
and  not  necessarily  the  cause,  we  can  better  understand  some 
of  the  items  in  the  table.  We  see  clearly  what  it  is  that  lies 
behind  a  street  railway  franchise,  or  the  franchise  of  the 
underground  system  of  New  York  City.  It  must  be  the 
wealth  by  means  of  which  the  transportation  can  take  place. 
The  streets  which  the  railway  has  the  right  to  use  form  the 
necessary  means  for  its  transportation  services.  To  own 
the  streets  involves  the  possession  of  the  right  to  use  them 
for  transportation  purposes,  and,  when  this  right  is  given 
or  sold,  as  when  a  franchise  is  granted,  this  act  constitutes 
a  partial  surrender  of  the  ownership  of  the  streets. 

Again,  let  us  consider  the  case  of  a  promise.  The  physical 
means  of  fulfilling  a  promise  are  evidently  the  person  who 
made  the  promise  and  the  wealth  which  that  person  can  or 
will  use  for  that  purpose.  Thus,  a  debt  or  bond  secured 
by  a  mortgage  is  primarily  a  claim  upon  the  promisor  which 
he  may  satisfy  out  of  his  earnings  or  his  general  wealth. 
But  it  offers  this  great  advantage  over  other  forms  of 
indebtedness,  that  it  is  also  a  contingent  claim  upon  a 
specific  portion  of  the  promisor's  wealth,  which  may  be 
taken  in  payment  even  against  his  will,  if  the  promisor 
otherwise  fails  to  make  good  his  promise.  Here  the  means 
of  perfecting  the  right  evidenced  by  the  bond  include  the 
person  of  the  promisor,  his  general  wealth,  and  the  specific 
part  of  that  wealth  covered  by  the  mortgage.  On  the  other 
hand,  a  "labor  due"  is  principally  a  claim  upon  the  person 
of  the  laborer,  for  he  must  be  the  means  of  performing  the 
labor  required.  In  country  districts  farmers  are  often 
under  obligations  to  the  county  to  furnish  a  certain  amount 
of  roadwork  of  men  and  horses.  The  right  to  such  work 
is  a  species  of  property  belonging  to  the  county.  A  still 
better  example  is  found  in  cases  where  the  labor  or  services 
to  be  rendered  are  of  a  personal  or  artistic  character,  such 
as  the  singing  of  a  Patti  or  the  acting  of  a  Bernhardt ;  for, 
while  one  under  contract  to  lay  bricks  might  reasonably 


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28  NATURE    OF    CAPITAL   AND   INCOME  [CHAP.  II 

fulfil  his  contract  by  furnishing  another  equally  skilful 
bricklayer,  no  audience  attracted  by  either  of  those  artists 
would  accept  in  return  for  its  entrance  money  the  perform- 
ance of  any  understudy,  no  matter  how  capable.  This 
right  to  the  services  of  a  particular  person,  as  distinguished 
from  the  right  to  services  of  a  particular  character,  gives 
rise  to  many  curious  cases  in  law.  Similarly,  a  personal 
note  is  to  a  large  extent  a  claim  upon  the  person  of  the 
drawer,  though  also  a  claim  upon  his  other  wealth;  for 
both  the  man  himself  and  his  external  wealth  are  the  means 
of  keeping  good  the  promise  and  finally  paying  the  debt. 
Another  case  is  that  of  a  "factor's  agreement"  or  some 
other  promise  by  which  a  firm  or  person  agrees  to  refrain 
from  certain  acts,  such  as  selling  in  competition  with  the 
promisee.  Some  years  ago  a  paper  manufacturer  near  New 
Haven  was  offered  a  round  sum  if  he  would  close  his  mills. 
This  he  did,  to  the  benefit  of  both  himself  and  his  former 
rivals,  though  not  of  the  public.  In  this  case  the  contract 
which  he  made  with  his  rivals  constituted  a  kind  of  prop- 
erty for  them;  the  wealth  by  means  of  which  his  promise 
was  made  good  was  evidently  his  own  person,  together  with 
his  plant ;  and  the  service  performed  was  the  inactivity  of 
both. 

Good  will  is  a  less  certain  though  still  a  valuable  form 
of  property.  A  few  years  ago  one  of  the  largest  newspapers 
in  the  United  States  was  sold.  The  property  included, 
besides  presses,  type,  linotype  machines,  office  building,  etc., 
the  items  of  overdue  subscriptions  and  good  will.  An  over- 
due subscription  is  a  debt  which  constitutes  a  virtual  prom- 
ise of  the  subscriber,  and  thousands  of  these  in  the  aggre- 
gate make  up  a  considerable  value.  By  good  will  is  meant 
something  very  similar;  namely,  the  quasi-promise  of  the 
subscribers  to  continue  to  pay  as  long  as  the  newspaper  is 
sent  to  them  and  they  are  satisfied.  These  quasi-promises 
are  also  property,  being  almost  equivalent  to  a  signed  agree- 
ment of  the  subscribers  to  the  effect :  "We  hereby  promise 


SEC.  6]  PROPKRTY  29 

to  pay  the  annual  sum  of  SS  to  the  -  -  Publishing  Com- 
pany, provided  that  and  so  long  as  its  newspaper  is  received 
and  is  satisfactory."  Thus  good  will  is  merely  the  right 
to  a  tacit,  loose,  and  contingent  promise  of  support  and  pat- 
ronage, less  cost.  The  firm  possessing  good  will  owns  a 
precarious  yet  valuable  claim  upon  its  patrons,  namely, 
the  chance  of  their  continued  patronage.  The  persons  of 
these  subscribers,  and  their  other  wealth,  are  what  under- 
lie the  property  right,  because  they  are  the  means  to  the 
desired  services  to  which  those  rights  apply.  Of  course 
the  chance  of  obtaining  these  services  is  very  much  less 
than  it  would  be  if  the  services  were  specifically  promised; 
but  chance,  either  large  or  small,  is  involved  in  all  property 
rights. 

In  the  same  way,  the  "custom"  of  a  tailor  or  the  "prac- 
tice" of  a  physician  is  simply  the  right  to  the  chance  of 
future  patronage. 

A  franchise  in  the  sense  of  a  monopoly  privilege  granted 
by  a  government  is  quite  different  from  a  street  railway 
franchise.  The  object  of  the  monopoly  is  to  prevent  cer- 
tain acts  of  certain  persons.  The  means  to  that  end  are, 
in  the  last  analysis,  the  persons  who  are  constrained  to 
refrain,  and  the  wealth  withdrawn  from  competition. 

We  may  similarly  regard  a  copyright.  Recalling  the 
case  of  the  paper  trust,  part  of  whose  property  was  the  prom- 
ise of  a  paper  manufacturer  not  to  compete,  we  may  regard 
a  copyright  as  the  right  to  a  similar  refraining  from  or  re- 
straining of  competition.  At  one  time,  an  English  pub- 
lisher would  obtain  the  promise  of  an  American  publisher 
not  to  "pirate"  his  works.  It  would  have  been  property 
of  great  value  to  the  publishers  of  the  Encyclopaedia  Bri- 
tannica  if  they  could  have  prevented  the  pirating  of  their 
work  in  this  country.  Prevention  can  now  be  accomplished 
through  the  instrumentality  of  international  copyright. 
The  wealth  underlying  this  property  right  is  the  wealth 
which,  if  employed  in  the  specified  line,  would  enter  into 


30  NATURE    OF   CAPITAL    AND    INCOME  [CHAP.  II 

competition  with  the  property  owner.  It  mainly  consists 
of  the  persons  and  plants  of  possible  competing  publishers  ; 
and  it  does  not  matter  whether  their  inactivity  —  their  non- 
competition —  is  purchased  by  a  money  payment  or  en- 
forced by  government  intervention. 

In  like  manner  we  may  resolve  the  problem  of  irre- 
deemable paper  money.  Where  this  exists  in  its  purest 
form,  with  no  promise  or  intention  of  ultimate  redemption 
by  the  government  which  issues  it,  it  amounts  to  a  forced 
loan,  or  rather,  a  levy.  It  is  like  a  check  drawn  by  the  gov- 
ernment upon  the  public,  which  each  individual  is  obliged 
to  cash.  It  is  an  order  to  surrender  on  demand  a  certain 
amount  of  the  community's  goods.  The  government  usu- 
ally employs  paper  money  to  obtain  ammunition  or  sol- 
diers' supplies.  The  merchants  who  give  these  goods  are 
forced  to  accept  paper  money  in  return,  and  allowed  to 
recoup  themselves  by  passing  on  these  orders  to  others. 
In  this  way  people  are  deluded  into  believing  that  no  one 
really  loses,  but  that  the  loss  is  perpetually  passed  on.  The 
loss  is  shifted,  but  nevertheless  it  exists ;  for,  since  a  definite 
quantity  of  supplies  has  been  abstracted  from  the  public 
by  the  government,  it  is  clear  that  this  much  loss  has  been 
suffered,  however  it  may  be  distributed  by  rotation.  Thus, 
irredeemable  paper  money  is  a  claim  on  the  general  wealth 
of  a  community.  Of  course  it  seldom  occurs  that  it  con- 
tinues irredeemable,  and  when  it  becomes  redeemable  it 
changes  its  character;  for  when  the  government  assumes 
the  obligation  involved,  it  becomes  a  special  claim  upon 
the  government  gold  and  other  wealth. 

A  somewhat  similar  vague  property  right  is  the  govern- 
ment's taxing  power,  which  is  the  right  to  take  from  the 
individual  so  much  of  the  services  or  product  of  his  wealth 
as  may  be  necessary  for  the  public  good.  The  heavier 
the  tax,  the  greater  the  reduction  in  the  value  of  the  in- 
dividual wealth  of  the  community.  It  is  well  known 
that  to  nationalize  land,  as  Henry  George  proposed,  means 


SEC.  7]  I'UOI'KKTY  31 

merely  to  increase  the  tax  upon  it  until  all  its  value  has 
been  taxed  out  of  it ;  that  is,  to  take  from  the  individual 
all  of  the  services  or  profit  of  his  landed  wealth  for  the  bene- 
fit of  the  public,  leaving  him  merely  the  empty  shell  of 
nominal  ownership.  The  case  is  analogous  to  that  of  a  per- 
son or  a  community  which  has  mortgaged  its  wealth  so 
heavily  that  the  value  of  its  services  is  entirely  consumed 
in  the  payment  of  interest,  and  nothing  is  left  with  which 
to  redeem  the  pledge.  The  same  principle  applies  to  all 
taxes,  even  when  not  carried  to  such  an  extreme. 

§7 

A  second  helpful  guide  in  resolving  the  various  obscure 
forms  of  property  is  found  in  the  fact  that  one  property  right 
is  often  overlaid  by  another.  For  instance,  a  mill  is  owned  in 
shares;  a  railway  company  owns  some  of  those  shares;  a 
bank  owns  some  of  the  railway  shares;  and  John  Smith 
owns  some  of  the  bank  shares.  It  is  evident  that  John 
Smith  has  a  claim  upon  the  wealth  constituted  by  the  mill, 
although  his  property  is  only  distantly  connected  with  it, 
and  through  several  intermediate  layers  of  property  rights. 

A  common  example  of  such  secondary  relation  between 
wealth  and  property  occurs  when  the  property  is  held  in 
trust.  At  common  law,  the  trustee  is  the  legal  owner;  but 
the  law  of  equity  recognizes  the  fact  that  the  beneficiary  is 
the  true  owner.  He  has  a  claim  against  the  trustee,  and  the 
trustee  holds  the  right  to  the  wealth  as  against  the  rest  of 
the  world.  The  beneficiary  must  work  out  his  rights 
through  the  rights  of  the  trustee. 

Another  good  example  is  that  of  a  claim  upon  a  govern- 
ment, as,  for  instance,  a  government  bond.  This  is  really 
a  claim  against  the  community,  for  the  government  is 
merely  an  intermediary  between  the  bondholder  and  the 
public  wealth  which  is  taxed  to  satisfy  the  bondholder's 
claims.  The  government  owns  property  only  as  a  sort  of 
trustee  for  the  public.  The  Boston  Common  is  held  by  the 


32  NATURE    OF   CAPITAL   AND    INCOME  [CHAP.  II 

city  of  Boston,  but  is  really  owned  by  the  citizens,  who  are 
the  true  beneficiaries.  Each  individual  who  has  the  right 
to  enjoy  it  is  to  that  extent  a  part  owner. 

It  is  not  uncommon  thus  to  have,  between  a  property 
right  and  the  wealth  underlying  it,  several  layers  of  prop- 
erty. A  man  who  owns  an  ordinary  foreign  bank  note  has 
a  claim  upon  the  property  of  the  bank.  But  the  bank's 
property  consists,  for  the  most  part,  not  of  tangible  wealth, 
but  of  promissory  notes  and  other  claims  on  merchants. 
These  notes  represent  a  part  right  in  the  wealth  (including 
persons)  of  the  community;  consequently  the  holder  of  a 
bank  note  quite  unconsciously  owns  a  claim  upon  the  dry 
goods,  groceries,  and  other  wealth  of  merchants,  which  make 
good  the  debts  of  these  merchants  to  the  bank. 

In  the  case  of  United  States  bank  notes  he  also  owns  an 
alternative  claim  on  government  bonds,  and  therefore  on 
the  taxable  wealth  which  makes  these  bonds  good.  It  is 
erroneous  to  think  of  a  bank  note  as  representing  simply 
money.  This  is  true  of  gold  certificates;  for  there  are  in 
the  United  States  Treasury  as  many  actual  gold  dollars  as 
there  are  certificates  in  circulation.  A  bank  note,  on  the 
other  hand,  is  made  good,  not  solely  by  the  metallic  reserve 
of  the  bank,  but  also  by  the  other  property  or  "assets," 
which  the  bank  is  constantly  changing  or  transforming  into 
cash.  The  Bank  of  England,  for  instance,  had  £60,000,000 
of  notes  out  at  a  given  date,  and  only  £43,000,000  of  gold 
in  its  vaults.  But  the  £17,000,000  deficiency  which  thus 
seemed  to  exist  was  represented  by  securities,  that  is,  other 
property  held  by  the  bank. 


A  third  guide  is  that  the  correspondence  between  prop- 
erty and  wealth  is  a  contemporaneous  correspondence. 
That  is  to  say,  the  existing  property  rights  are  rights  to 
the  use  of  existing  wealth,  so  that  existing  wealth  underlies 
all  existing  property  rights.  It  would  seem  at  first  sight 


SEC.  8]  PROPERTY  33 

that  "credit"  forms  an  exception,  for  credit  is  a  present 
right  to  a  future  payment.  But  it  is  impossible  to  have  a 
right  to  any  future  wealth  which  is  not  also  a  right  to  some 
present  wealth  as  a  means  of  securing  that  future  wealth. 
The  right  to  next  year's  fruit  is  a  right  to  or  in  present  fruit 
trees.  The  right  to  next  year's  wheat  is  a  right  to  or  in  the 
present  farm,  farmer,  and  farm  implements.  The  right  to 
receive  a  future  chair  or  table  yet  unmade  is  the  right  to  or 
in  the  present  person,  tools,  and  other  wealth  of  the  car- 
penter, which  are  the  means  by  which  that  chair  or  table 
is  to  be  secured.  To  own  a  note  falling  clue  next  year  is 
a  part  right  in  the  person  and  other  "assets"  of  the  prom- 
isor, and  ceases  to  have  value  as  soon  as  he  ceases  to  be 
"good  for  it."  The  courts  do  not  restrict  a  debtor  in  the 
disposition  of  his  possessions  prior  to  the  maturity  of  a  note. 
He  may  elect  to  squander  these,  and  even  to  commit  sui- 
cide. But  such  destruction  of  the  present  means  of  pro- 
viding for  future  payment  carries  with  it  the  impairment 
or  destruction  of  the  value  of  the  note.  No  future  com- 
modities or  benefits  whatever  can  be  owned  in  the  present 
except  as  claims  on  certain  requisites  of  their  production 
now  in  existence.  We  cannot  own  next  year's  goods  sus- 
pended in  mid  air,  as  it  were,  any  more  than  we  can  fly  a 
kite  without  a  cord.  There  must  always  be  some  present 
means  of  controlling  the  future.  Thus,  credit,  like  every 
other  property  right,  is  a  part  right  upon  existing  wealth. 
And  not  only  is  every  right  to  a  future  benefit  a  claim 
on  present  wealth,  but  conversely,  every  claim  on  present 
wealth  is  a  right  to  a  future  benefit.  Owning  rights  to 
"futures"  is  therefore  not  an  exceptional  case,  but  the  gen- 
eral one.  As  we  have  seen,  all  wealth  is  merely  existing 
means  toward  future  services,  and  all  property,  merely  pres- 
ent rights  to  some  of  those  future  services.  It  is  only 
through  the  future  services  that  wealth  and  property  are 
bound  together  at  all.  The  sequence  of  ideas  is,  first,  pres- 
ent wealth ;  second,  future  services ;  third,  present  rights  to 


34  NATURE    OF   CAPITAL   AND   INCOME  [CHAP.  II 

these  future  services  and  therefore  to  the  present  wealth 
which  yields  them.  Property  is  thus  always  a  right  to  the 
chance  of  a  future  benefit.  It  always  contemplates 
both  present  and  future  time.  We  are  here  emphasiz- 
ing the  fact  that  property  always  constitutes  an  inter- 
est in  the  present  means  for  acquiring  it.  Property  in 
nothing  is  nothing.  This  principle  applies  even  to  the 
extreme  case  of  good  will.  We  saw  that  good  will  is  the 
ownership  of  a  chance  of  continued  patronage.  The  future 
patronage  may  in  some  cases  include  that  of  persons  yet 
unborn;  but  the  road  to  their  patronage  must  lie  through 
the  present  generation.  Existing  persons  and  things  must 
always  constitute  the  means  for  the  attainment  of  any 
benefits  expected  in  the  future. 

§  9 

A  fourth  guide  is  that,  in  the  case  of  partial  ownership 
of  wealth,  the  aggregate  of  all  the  partial  rights  constitutes 
the  total  ownership.  WTe  may  picture  to  ourselves  all  ar- 
ticles of  wealth  as  having  attached  to  them  streams  of 
services  stretching  out  into  the  future.  These  services 
are  cut  up  among  separate  owners  in  different  ways,  some- 
times transversely,  sometimes  longitudinally,  and  some- 
times definite  parts  of  them  are  separated  out.  The  total 
ownership  of  the  wealth  is  simply  the  aggregate  of  the  rights 
to  the  entire  stream  of  future  services.  It  may,  of  course, 
be  true  that  the  character  and  size  of  this  stream  of  services 
will  differ  according  to  the  different  methods  by  which 
its  ownership  is  parceled  out.  This  fact,  however,  does 
riot  invalidate  the  principle  that  the  total  ownership  is 
the  combination  of  all  the  partial  rights. 

In  common  speech  the  minor  rights  to  wealth  are  not 
ordinarily  dignified  as  rights  of  ownership.  Thus,  a  ten- 
ant's right  in  the  dwelling  he  occupies  is  sharply  distin- 
guished from  the  right  of  the  owner.  Yet  the  law  recog- 
nizes a  leasehold  as  an  estate  in  the  land,  and  when  the 


SEC.  9]  PROPP:RTY  35 

owner  of  land  wishes  to  sell  and  convey  an  unencumbered 
fee  simple  title,  he  finds  it  necessary  to  extinguish  all  out- 
standing leases,  or  claims  for  future  services,  often  at  con- 
siderable cost.  Recently  the  New  York  Reform  Club 
sold  its  leasehold  in  a  building  for  $25,000,  because  the  pur- 
chaser could  not  afford  to  wait  for  the  expiration  of  the 
lease.  The  total  ownership  always  includes  the  ownership 
of  the  tenant. 

In  like  manner,  the  total  value  of  any  concrete  wealth 
is  the  total  value  of  the  property  rights  in  it.  The  close 
correspondence  between  wealth  and  property  gives  us  a 
new  method  of  appraising  wealth,  namely,  by  appraising 
the  property  rights  to  it.  In  fact,  we  are  here  provided 
with  another  sense  of  appraisement  of  wealth,  in  addition 
to  the  several  already  given  in  Chapter  I.  Such  appraise- 
ment may  mean,  not  what  the  whole  article  of  wealth 
would  sell  for  en  bloc,  but  the  sum  of  the  values  of  the  par- 
tial rights  to  it  when  these  latter  are  appraised  on  the  basis 
of  small  individual  sales.  Thus,  the  value  of  a  railroad, 
operating  under  normal  conditions,  is  found  by  taking  the 
sum  of  the  values  of  its  stocks  and  bonds.  Railways  are 
seldom  sold  as  a  whole,  but  their  stocks  and  bonds  are 
constantly  on  the  market,  and  are  often  the  only  means  of 
affording  a  valuation. 

It  is  true  that  under  these  circumstances  the  market  price 
of  the  stock  would  form  no  basis  for  judging  what  would 
be  the  value  of  the  road  if  sold  as  a  whole.  There  would 
need  to  be  added  the  value  of  "control."  But  this  will 
be  accounted  for  by  an  addition  to  the  value  of  such  of  the 
shares  as  will  secure  this  control.  "Control"  is  the  power, 
coming  from  a  majority  of  votes,  to  obtain  from  the  road 
some  services  which  would  not  be  possible  without  such 
majority  ownership.  The  additional  benefit  thus  obtained 
may  be  illegitimate,  as  when  the  parties  in  control  vote 
themselves  large  salaries.  But  whether  legitimate  or  ille- 
gitimate, the  power  to  make  the  road  better  serve  one's 


36  NATURE    OF   CAPITAL   AND   INCOME  [CiiAi-.  II 

interest  often  affects  profoundly  the  value  of  the  shares. 
The  stock  of  the  Chicago,  Burlington,  and  Quincy  Railroad 
was  quoted  at  $132  when  a  certain  capitalist  determined  to 
buy  it.  Knowing  that  it  would  be  almost  impossible  to 
acquire  all  the  stock  by  ordinary  means,  he  offered  instead 
to  take  over  as  much  as  should  be  offered  to  him,  provided 
it  was  more  than  half,  and  to  give  $200  in  four  per-cent 
bonds  for  each  $100  share, — an  offer  which  was  accepted  by 
most  of  the  stockholders.  The  acceptance  added  at  once 
fifty  per  cent  to  the  market  value  of  the  stock,  and  improved 
even  the  value  of  the  bonds ;  so  that  the  value  of  the  system, 
sold  virtually  as  a  whole,  was  much  more  than  of  the  stock 
and  bonds  before  the  negotiation  was  opened.  The  valua- 
tion of  the  road  will  thus  be  different  according  to  whether 
it  is  under  the  control  of  a  particular  interest  or  whether 
its  ownership  is  widely  distributed,  as  well  as  according  to 
the  purpose  for  which  the  valuation  is  made.1  But  in  every 
instance  the  value  of  the  railroad  is  the  sum  of  the  values 
of  the  complete  aggregate  of  rights  in  it. 

If  one  bears  in  mind  the  explanations  which  have  been 
given,  there  can  scarcely  be  any  difficulty  in  tracing  out  for 
each  property  right  some  underlying  wealth,  so  that  we  may 
give  adherence  to  the  general  principle  that  wealth  and  prop- 
erty are  coextensive.  That  this  is  true  as  a  "general  fact" 
cannot  fail  to  be  admitted  even  were  it  necessary  to  reject 
it  as  a  "necessary  truth."  But  if  our  definitions  of  wealth 
and  property  are  adopted,  it  becomes  also  a  necessary  truth. 

§  10 

Having  seen  what  property  is,  we  may  now  classify 
property  rights.  There  are  two  chief  classes,  complete 
rights  and  partial  rights.  A  complete,  or  practically 
complete,  right,  or  "fee  simple"  to  an  article  of  wealth,  is  a 
right  to  all  those  uses  of  that  article  which  are  owned;  a 

1  The  completes!  account  of  railway  valuation  is  that  contained 
in  Bulletin  21,  "The  Commercial  Valuation  of  Railway  Operating 
Property,"  United  States  Census,  1905. 


Sue.  10] 


PROPERTY 


37 


partial  right  is  a  right  to  a  part  of  its  uses.  The  partial 
rights  are  the  only  ones  which  make  difficulty. 

The  services  of  an  article  of  wealth  may  be  apportioned 
among  different  part  owners  in  many  ways.  If  they  are 
divided  longitudinally  in  time,  the  rights  of  the  various 
coowners  are  similar  to  each  other.  The  chief  examples 
are  the  rights  of  partners  and  stockholders,  and  the  less 
well-defined  rights  of  the  individual  members  of  a  club, 
family,  or  commune  to  the  common  property  and  all  rights 
in  common,  and,  finally,  the  rights  to  the  different  kinds  of 
uses,  as,  for  instance,  where  one  person  owns  the  right  of 
farming  a  piece  of  land,  another  the  right  of  mining  its 
minerals,  and  a  third  the  right  of  fishing  in  the  streams 
which  run  through  it. 

If  the  services  are  divided  transversely  in  time,  one  per- 
son has  the  rights  of  all  services  up  to  a  particular  date, 
and  another  all  the  rights  beyond  that.  The  former 
person  is  called  the  tenant  and  the  latter  the  landlord. 

If  the  services  are  limited  both  in  time  and  also  in  quantity 
or  value,  we  have  still  another  group  of  property  rights. 
These  and  other  classes  are  seen  in  the  following  scheme 
of  classification. 


>.  -I 


Complete  (Fee  Simple) 

to  services  cut  longitudinally 


to  services  cut  transversely 


.  Partial 


(  rights  in  common 
rights  to  different 

usufructs 
partnership  rights 
joint  stock  shares 

lease 

reversion 

patent  and  copyright 

f  bonds 

I  private  notes 


rights  to  definite  parts 
of  services 


bank  note: 
{ bank  deposits 


t  orders 


f  checks,    drafts,  and 

bills  of  exchange 
irredeemable    paper 
money 


.  minor  and  indefinite 


f  good  will  and  custom 
I  taxing  power 


38  NATURE    OF   CAPITAL   AND   INCOME  [CHAP.  II 


Since  wealth  and  property  are  each  the  opposite  aspect 
of  the  other,  economics  might  be  described  as  the  "sci- 
ence of  property"  quite  as  truly  as  the  "science  of  wealth." 
If  we  are  studying  the  economic  condition  of  a  whole 
country,  we  prefer  to  fix  our  attention  upon  wealth,  caring 
less  about  how  its  ownership  is  divided.  We  are  then  inter- 
ested in  the  acreage  of  wheat  fields,  the  extent  of  coal 
mines,  railways,  factories,  and  homesteads,  and  not  in  their 
owners.  On  the  other  hand,  if  we  are  studying  the  "  dis- 
tribution of  wealth"  -the  condition  of  individuals  or  of 
classes  —  it  is  property  on  which  we  need  to  fix  attention. 
The  idea  of  wealth,  therefore,  is  associated  with  the  wel- 
fare of  the  community  in  general,  while  that  of  property 
is  associated  with  the  welfare  of  the  different  individuals 
in  the  community. 

But,  it  may  be  asked,  why  is  so  much  stress  laid  on 
the  principle  that  wealth  and  property  are  coextensive? 
It  may  be  conceded  that  most  of  the  principles  of  political 
economy  will  be  unaffected  whether  or  not  this  one  is  ac- 
cepted as  rigorously  true.  Its  usefulness  consists  in  help- 
ing us  to  arrange  our  ideas.  At  present  there  seems  to 
exist  in  the  popular  mind  a  confusion  of  the  concepts  of 
wealth,  property,  certificates  of  property,  services,  and  utility, 
all  of  which  should  be  carefully  separated  from  each  other. 
No  one  can  fully  understand  monetary  problems,  for  instance, 
unless  he  distinguishes  carefully  the  three  elements  to  which 
the  term  "money"  is  indiscriminately  applied.  There  is 
money-wealth,  such  as  a  gold  eagle;  money-property,  such 
as  the  right  of  a  holder  of  "greenbacks";  and  money-cer- 
tificates,  such  as  the  paper  "greenbacks"  themselves.  If 
the  fact  that  wealth  and  property  are  coextensive  were  more 
generally  known  and  acknowledged,  some  very  practical  and 
salutary  results  would  follow.  Wild  schemes  of  currency 
inflation,  which  are  based  on  the  idea  that  wealth  may  be 


SEC.  11]  PROPERTY  39 

increased  simply  by  multiplying  the  titles  to  it,  would  be 
checked,  and  the  usual  atrocities  of  double  taxation,  for  in- 
stance, of  farm  and  mortgage,  or  of  railways  and  railway 
shares,  would  be  avoided.1 

If  we  bear  in  mind  the  distinctions  in  this  and  in  the 
previous  chapter,  we  shall  see  that  there  is  no  advantage, 
but  much  disadvantage,  in  including  any  "immaterial" 
elements  in  wealth.  "Immaterial  wealth"  is,  in  fact,  one 
of  those  bugaboos  which  have  done  a  great  deal  to  obscure 
the  simplicity  of  economic  relations.  Legal  advice  or 
medical  attendance  are  not  "immaterial  wealth  " ;  they  are, 
as  we  have  seen,  simply  services  of  wealth  (human  wealth 
in  this  case).  The  "properties  and  powers  of  nature" 
are  not  wealth,  but,  as  explained  in  the  previous  chapter, 
are  attributes  of  land  and  enter  economic  science  merely 
as  giving  characterization  to  that  particular  kind  of  wealth. 
They  cannot  be  counted  as  wealth  in  addition  to  the  land 
any  more  properly  than  can  the  elasticity  of  rubber  be 
counted  as  wealth  in  addition  to  the  rubber.  Likewise, 
swift  horses  are  wealth,  but  not  their  swiftness;  honest,  wise, 
successful,  and  healthy  men  are  wealth,  but  not  their  hon- 
esty, wisdom,  skill,  or  health.  Most  of  the  mystery  of 
banking  to  the  ordinary  mind  consists  in  the  mistaken  no- 
tion that  credit  is  something  "inflated/'  without  a  tangible 
basis,  A  mere  inspection  of  a  bank's  balance  sheet  should 
serve  to  make  clear  the  fact  that  behind  every  claim  upon 
the  bank  is  something  to  make  it  good.  If  the  anterior 
something  be  itself  a  claim  on  some  other  bank  or  person, 
there  lies  behind  it,  in  turn,  some  basis,  and  so  on  until  a 
concrete  instrument  is  finally  found. 

Another  common  error  is  the  belief  that  "wealth  con- 
sists of  utility."  If  this  were  true,  the  law  of  diminishing 

1  See  Report  of  Professor  Edward  W.  Bemis  and  Carl  H.  Xau,  on 
Value  of  Ohio  Railroads,  1903;  also,  Report  of  the  Interstate  Com- 
merce Commission  on  Railways  in  the  United  States  in  190:2,  1903, 
Part  V. 


40  NATURE   OF   CAPITAL   AND   INCOME  [CHAP.  II 

utility,   that  equal  increments  of  wealth  have  decreasing 
increments  of  utility,  would  be  a  contradiction  in  terms. 

To  plead  in  extenuation  of  such  confusions  the  fact  that 
popular  usage  is  guilty  of  them,  is  like  trying  to  justify  in 
the  science  of  physics  a  jumbling  together  of  the  concepts 
of  mass  and  density,  or  of  velocity  and  acceleration,  or  of 
force  and  energy,  on  the  ground  that  the  ordinary  man  does 
not  distinguish  between  them.  The  proper  method  of 
avoiding  large  errors  in  any  science  is  to  avoid  small  ones 
at  the  outset.  This  can  be  accomplished  only  by  scrupu- 
lous attention  to  elementary  distinctions. 


CHAPTER  III 

UTILITY 


WE  have  seen  that  all  wealth  and  property  imply  pro- 
spective services  or  "desirable  events."  It  is  the  desir- 
ability of  these  future  expected  services  which  gives  meaning 
to  all  economic  phenomena.  It  would  therefore  be  im- 
possible, in  any  full  view  of  the  subject,  to  confine  our- 
selves strictly  to  the  study  of  objective  wealth,  property, 
and  services.  In  the  present  chapter  we  shall  consider 
briefly  the  subjective  or  psychical  element  in  economics. 

Wealth  is  wealth  only  because  of  its  services ;  and  serv- 
ices are  services  only  because  of  their  desirability  in  the 
mind  of  man,  and  of  the  satisfactions  which  man  expects 
them  to  render.  Indeed,  the  desirability  of  services  is 
implied  in  their  very  definition  as  "desirable  events." 
The  mind  of  man  supplies  the  mainspring;  in  the  whole  eco- 
nomic machinery.  It  is  in  his  mind  that  desires  originate, 
and  in  his  mind  that  the  train  of  events  which  he  sets 
going  in  nature  comes  to  an  end  in  the  experience  of  sub- 
jective satisfactions.  It  is  only  in  the  interim  between  the 
initial  desire  and  the  final  satisfaction  that  wealth  and  its 
services  have  place  as  intermediaries. 

We  are  thus  led  to  consider  two  new  concepts,  —  that 
of  "  desirability "  and  that  of  "  satisfaction."  Both  of 
these  enter  into  our  consideration  only  as  they  are  applied 
to  the  three  economic  elements,  —  wealth,  property, 
services.  To  avoid  unnecessary  repetitions,  we  may  treat 
these  three  elements  under  the  one  rubric  of  "goods." 

41 


42  NATURE    OF   CAPITAL   AND    INCOME          [CHAP.  Ill 


The  desirability,  then,  of  any  particular  goods,  at  any 
particular  time,  to  any  particular  individual,  under  any 
particular  conditions,  is  the  strength  or  intensity  of  his  de- 
sire for  those  goods  at  that  time  and  under  those  conditions. 
What  is  here  called  desirability  is  identical  with  what  has 
usually  been  called  in  economic  writings  "utility."  But 
utility,  though  not  to  be  utterly  displaced,  is  not  the  hap- 
piest term  for  our  purpose.  To  say  nothing  of  the  mere 
awkwardness  of  its  only  antithetical  term  —  "disutility" 
—  as  compared  with  "undesirability,"  it  has  fallen  heir 
to  so  many  different  meanings  that  its  use  here  is  apt  to 
be  confusing.  The  term  "useful,"  for  instance,  in  ordinary 
language  is  employed  in  opposition  to  "ornamental." 
In  this  sense  diamonds  are  said  to  be  ornamental  and  not 
useful,  though  in  economic  science  they  are  adjudged 
useful.  Again,  "utility"  usually  implies  intrinsic  merit, 
whereas,  when  we  employ  it  in  economic  science,  we  are 
obliged  to  apply  it  to  any  noxious  thing  considered  by  its 
owner  desirable,  for  instance,  opium,  alcohol,  or  degrad- 
ing literature.  Finally,  in  the  last  few  years,  the  word 
"utility"  has  come  into  a  new  and  technical  meaning  as 
employed  in  the  phrase  "public  utilities,"  which  desig- 
nates electric  lighting  plants,  street  railway  systems,  gas 
works,  and  many  other  things  which  are  merely  collections 
of  wealth  of  a  peculiar  kind. 

In  order  to  obviate  these  objections,  Professor  Pareto 
has  proposed  an  entirely  new  term,  "ophelimity."  This 
has  both  the  advantages  and  the  disadvantages  of  any 
newly  invented  technical  term,  and  has  thus  far  shared 
the  fate  which  usually  befalls  the  attempt  to  coin  words. 
The  word  "utility"  is  still  employed,  and  it  is  not  likely 
that  "desirability,"  "ophelimity,"  or  any  other  term  will 
soon  displace  it.  In  the  present  book  we  shall  use  both 
"utility"  and  "desirability,"  but  preferably  the  latter. 


SEC.  3]  UTILITY  43 

In  proposing  that  economists  substitute  so  far  as  possible 
the  term  "desirability"  for  "utility,"  the  author  is  simply 
following  the  example  of  Professor  Gide  1  and  Professor 
Marshall. 

§0 
3 

If  the  term  "utility"  is  to  be  used  at  all,  we  must  dis- 
tinguish the  utility  of  goods  from  the  use  of  the  goods. 
As  has  been  pointed  out,  the  uses  or  services  of  goods  are 
the  desirable  events  which  occur  by  their  means.  Utility, 
on  the  other  hand,  is  not  these  desirable  events,  but  their 
desirability. 

Again,  the  desirability  or  utility  of  goods  must  not  be 
confused  with  the  pleasure  which  may  be  ultimately  ob- 
tained from  those  goods.  Here  our  second  concept  is 
involved,  for  pleasure  is  not  the  desire,  but  the  satisfac- 
tion of  the  desire.  It  is  an  experience  in  time,  and  requires 
duration  of  time  for  its  existence.  Desirability,  which 
means  the  intensity  of  desire  of  an  individual  under  certain 
conditions,  merely  indicates  a  state  of  mind  at  a  particular 
point  of  time,  namely,  the  point  of  time  at  which  he  mentally 
weighs  and  measures  the  desirability  of  any  contemplated 
service,  property,  or  wealth.  We  may  speak  of  the  de- 
sirability of  a  fruit  orchard  to  a  particular  person  on  Janu- 
ary 1,  1905;  but  the  pleasure  derivable  from  that  orchard 
is  only  to  be  experienced  during  future  years,  as  it  bears 
fruit  and  the  fruit  gives  enjoyment  to  those  who  eat  it. 
Thus  we  have  two  concepts :  utility  or  desirability,  —  a 
state  of  mind  at  a  point  of  time :  and  pleasure  or  satisfac- 
tion, —  an  experience  of  mind  through  a  period  of  time. 
These  two  concepts  are  closely  related ;  for  the  desirability 
of  goods  is  simply  the  present  esteem  in  which  the  future 

1  Gide's  Principles  of  Political  Economy,  2d  American  ed.,  1904, 
p.  48.  See  also  the  present  writer's  "  Mathematical  Investigations  in  the 
Theory  of  Value  and  Prices,"  Transactions  of  the  Connecticut  Academy, 
1892,  p.  23. 


44  NATURE    OF   CAPITAL   AND   INCOME          [CHAP.  Ill 

satisfactions  from  those  goods  are  held.  But  the  two  are 
none  the  less  distinct.  It  is  with  utility  or  desirability 
that  we  are  concerned  in  this  chapter. 

§4 

The  desirability  of  any  particular  goods  may  relate  to 
the  whole  or  to  any  part  of  the  group  of  goods.  The  de- 
sirability of  the  entire  group  is  called  the  total  desirability ; 
the  desirability  of  one  unit  more  or  less  of  the  group  is 
called  the  marginal  desirability.  In  economic  science  we 
have  to  do  more  with  marginal  than  with  total  desirability, 
and  it  is  important  that  the  concept  of  marginal  desir- 
ability should  be  thoroughly  understood. 

That  marginal  desirability  is  the  desirability  of  one  unit, 
more  or  less,  may  be  illustrated  as  follows:  If  a  person 
possesses  ten  chairs,  their  marginal  desirability  is  the  differ- 
ence, in  his  mind,  between  the  desirability  of  having  ten 
chairs  and  the  desirability  of  having  nine  chairs;  that  is, 
it  is  the  desirability  sacrificed  by  having  one  chair  less. 
Or,  w7hat  is  almost  the  same  thing,  the  marginal  desirability 
of  the  group  of  ten  chairs  is  the  desirability  of  one  chair 
more,  —  the  difference  in  desirability  between  eleven  chairs 
and  ten.  Whether  the  marginal  desirability  is  taken  as 
referring  to  one  unit  more  or  to  one  unit  less  is  usually  of 
so  little  importance  as  not  to  require  separate  designations 
to  distinguish  them,  and  in  case  the  commodity  is  one  which 
admits  of  indefinite  subdivision,  as  flour,  wheat,  coal,  etc., 
the  two  coalesce  as  the  size  of  the  increment  is  reduced  in- 
definitely.1 This  fact  is  usually  expressed  by  saying  that 
the  marginal  desirability  of  the  chairs  is  the  desirability  of 
"the  tenth"  chair.  But  though  this  mode  of  statement  is 
correct,  it  is  not  intended  to  convey  the  idea  that  any  par- 
ticular chair  is  the  "tenth"  chair. 

The  group  of  goods  the  marginal  desirability  of  which  is 
under  consideration  may  be  any  specified  group  of  goods 

1  For  a  mathematical  treatment  see  Appendix  to  Chap.  Ill,  §  1. 


SEC.  4]  UTILITY  45 

whatever.  Reference  may  be  had  to  a  specified  group  of 
goods  now  existing,  or  to  a  specified  group  of  goods  in  the 
future,  or  to  a  specified  flow  of  goods  through  a  period  of 
time.  For  instance,  the  marginal  desirability  of  coal  to  an 
individual  may  be  taken  to  refer  to  the  particular  stock  of 
coal  in  his  bin  at  the  present  moment.  If  this  stock  con- 
sists of  fifteen  tons,  its  marginal  desirability  is  the  desir- 
ability of  the  fifteenth  ton,  or  the  difference  to  him  between 
the  desirability  of  having  fifteen  and  that  of  having  four- 
teen tons.  Or,  reference  may  be  had  to  an  intended  pur- 
chase of  coal  to  be  delivered  in  three  months.  If  we  con- 
sider a  possible  purchase  of  future  coal  to  the  extent  of 
fifteen  tons,  its  marginal  desirability  then  represents  the 
present  desire  for  the  fifteenth  ton,  in  exactly  the  same 
way  as  though  reference  were  had  to  an  existing  stock. 
Again,  if  a  person  is  consuming  in  his  household  fifteen  tons 
of  coal  a  year,  its  marginal  desirability  at  any  instant  is 
the  desirability  of  the  fifteenth  ton,  or  the  sacrifice  which 
would  be  occasioned  were  he  to  reduce  his  yearly  consump- 
tion from  fifteen  tons  to  fourteen. 

Again,  the  group  of  goods  considered  may  consist  of  ar- 
ticles all  of  which  are  of  the  same  kind,  or  of  a  heterogeneous 
collection.  In  the  preceding  examples  the  goods  were  of 
exactly  the  same  kind.  As  an  example  of  the  marginal 
desirability  of  a  group  consisting  of  diverse  kinds,  we 
may  cite  the  desirability  of  an  additional  monthly  magazine 
or  newspaper.  If  a  subscriber  is  already  taking  ten  periodi- 
cals of  different  kinds,  the  desirability  of  a  specified  journal 
additional  to  the  existing  assortment  may  be  regarded  as 
the  marginal  desirability  with  reference  to  the  entire  group 
of  journals. 

In  the  same  way  we  may  speak  of  the  marginal  desir- 
ability of  a  series  of  characteristics  or  features  connected  with 
any  article  or  articles  of  wealth.  A  person  contemplating 
the  building  of  a  house  may  have  to  decide  how  many  win- 
dows he  will  put  in.  If  he  contemplates  fifty  windows,  the 


46  NATURE   OF   CAPITAL   AND    INCOME          [CHAP.  Ill 

marginal  desirability  of  the  windows  is  the  desirability  of 
the  fiftieth  window,  or  the  difference  in  the  desirability 
of  having  fifty  windows  rather  than  forty-nine. 

§5 

The  first  principle  in  regard  to  marginal  desirability 
is  that  an  increase  in  the  quantity  of  goods  in  the  group 
the  marginal  desirability  of  which  is  under  consideration, 
results  in  a  decrease  in  the  marginal  desirability  of  the 
group.  Each  successive  increment  is  less  desirable  than 
the  preceding  increment.  The  marginal  desirability  of 
sugar  to  the  householder  consuming  five  pounds  weekly  is 
greater  than  the  marginal  desirability  if  six  pounds  are  con- 
sumed, and  is  successively  diminished  as  each  successive 
pound  is  added  to  his  consumption. 

It  is  well  to  remember  that  when  the  term  "successively" 
is  here  employed,  it  is  not  used  in  a  temporal  sense.  The 
succession  to  which  it  refers  is  not  a  succession  in  time,  but 
a  succession  in  thought.  We  consider  the  consumer  of 
sugar  under  a  series  of  different  hypotheses  which  we 
examine  successively.  We  begin  with  the  hypothesis  of 
a  weekly  consumption  of  five  pounds,  and  take  up  succes- 
sively the  hypotheses  of  six  pounds,  seven  pounds,  eight 
pounds,  etc.  The  desirability  of  the  "last"  pound  in  this 
series  is  the  marginal  desirability  for  the  group  ending  at 
that  point;  but  the  "last"  pound  refers  to  the  one  consid- 
ered last  in  our  mental  review,  and  not  the  one  acquired  last 
by  the  consumer.  This  fact  needs  to  be  emphasized,  in 
view  of  frequent  confusion  on  the  subject  occasioned  by  too 
loose  an  employment  of  the  words  "last "  and  "successive." 
It  is  presumably  because  of  the  time  confusions  involved 
in  these  words  that,  under  the  leadership  of  Wieser1  and 
Marshall,2  economists  have  substituted  the  phrase  "mar- 
ginal utility"  for  the  older  phrase  of  Jevons,  "final  utility." 

With  these  provisos  and  explanations  in  view,  it  is  clear 

1  Ursprung  des  Werthes,  p.   128. 

2  Principles  of  Economics,  3d  eel.,  1895,  p.  168. 


SEC.  5]  UTILITY  47 

that  the  total  desirability  of  any  group  of  goods  is  the  sum 
of  the  desirabilities  of  the  successive  units.  The  total 
desirability  of  the  ten  chairs,  for  instance,  is  found  by  add- 
ing together  (1)  the  desirability  of  having  only  one  chair, 
(2)  the  desirability  of  having  a  second  chair,  (3)  a  third, 
(4)  a  fourth,  etc.,  until  ten  chairs  have  been  considered. 
These  successive  desirabilities  will  evidently  continually 
diminish.  Hence  their  sum,  or  the  total  desirability  of  the 
group,  is  not  the  same  thing  as  ten  times  the  marginal  de- 
sirability. In  this  is  found  the  explanation  of  the  fact  that 
the  possessor  of  the  chairs  regards  them  as  possessing  much 
more  total  desirability  to  him  than  the  total  desirability 
of  the  money  which  they  cost,  although  the  loss  of  any  one 
of  the  ten  chairs  may  not  represent  more  desirability  than 
the  desirability  of  the  money  which  that  one  chair  cost.1 

As  is  well  known  to  all  students  of  the  modern  theory 
of  value,  marginal  desirability  lies  at  the  root  of  the  deter- 
mination of  value  and  price.  We  are  here  concerned, 
however,  not  in  applying  the  concept  of  marginal  desir- 
ability to  the  determination  of  economic  magnitudes,  but 
merely  in  explaining  its  nature. 

Although  the  definitions  which  have  been  given  of  de- 
sirability serve  to  explain  its  nature,  they  do  not  enable 
us  to  employ  it  in  a  quantitative  manner.  The  exact 
measurement  of  desirability  is  a  subject  of  much  impor- 
tance, as  well  as  of  great  difficulty.  Inasmuch  as  in  the 
present  work  only  an  incidental  use  will  be  made  of  these 
concepts,  it  does  not  seem  proper  here  to  enter  into  these 
discussions.2 

1  Cf.  Fetter's  Principles  of  Economics,  New  York,  1904,  pp.  25-26. 

2  See  the  writer's  "  Mathematical  Investigations  in  the  Theory  of 
Value  and  Prices,"  Transactions  of  the  Connecticut  Academy  of  Arts 
and  Sciences,  1893,  Vol.  IX;    Pigou,  Economic  Journal,  March,  1903, 
Vol.   XIII;    Pareto,    Cours   d' Economic   Politique,    Vol.    I;     Giornale 
d'Economisti,   August,    1892;    J.   B.   Clark,   "Ultimate  Standard  of 
Value,"    Yale    Review,    November,    1892;     Seligman,    Principles    of 
Economics,    Longmans,  Green  &  Co.,    1905,  Chap.    XIII;    Chin  tao 
Chen's  Societary  Circulation,  a  doctor's  thesis,  Yale  Univ.,  1906. 


PART  I.     CAPITAL 

CHAPTER  IV.  CAPITAL 

CHAPTER    V.  CAPITAL  ACCOUNTS 

CHAPTER  VI.  CAPITAL  SUMMATION 


CHAPTER  IV 

CAPITAL 


IN  the  foregoing  introduction  we  have  set  forth  several 
fundamental  concepts  of  economic  science,  —  wealth, 
property,  services,  satisfactions,  utility,  price,  and  value. 
We  have  seen  that  wealth  consists  of  material  appropriated 
objects,  and  property,  of  rights  in  these  objects ;  that  wealth 
in  its  broadest  sense  includes  human  beings,  and  property 
in  its  broadest  sense  includes  all  rights  whatsoever;  that 
services  are  the  benefits  of  wealth,  satisfactions  the  enjoy- 
ment of  services,  and  desirability  or  utility  the  desire  for 
wealth,  property,  services,  or  satisfactions;  that  prices  are 
the  ratios  of  exchange  between  quantities  of  wealth,  prop- 
erty, or  services;  and,  finally,  that  value  is  the  price  of  any 
of  these  multiplied  by  the  quantity.  These  concepts  are 
the  chief  tools  needed  in  economic  study. 

Nothing  has  yet  been  said  as  to  the  relation  of  these 
various  magnitudes  to  that  great  "  independent  variable  " 
of  human  experience,  time.  When  we  speak  of  a  certain 
quantity  of  wealth  we  may  have  reference  either  to  a  quan- 
tity existing  at  a  particular  instant  of  time,  or  to  a  quan- 
tity produced,  consumed,  exchanged,  or  transported  during 
a  period  of  time.  The  first  quantity  is  a  stock  (or  fund) 
of  wealth;  the  second  quantity  is  a  flow  (or  stream)  of 
wealth.  The  contents  of  a  granary  at  noon,  January  1, 
1906,  is  a  stock  of  wheat ;  the  amount  of  wheat  which  has 
been  hoisted  into  it  during  a  week,  or  the  amount  of  wheat 
which  has  been  exported  from  the  port  of  New  York  during 

51 


52  NATURE   OF   CAPITAL   AND   INCOME          [CHAP.  IV 

1905,  is  a  flow  of  wheat.  The  term  " wealth"  by  itself  is 
insufficient  to  determine  which  of  these  two  kinds  of  mag- 
nitudes is  meant.  Similarly,  when  we  speak  of  property 
or  of  value,  we  may  have  in  mind  either  a  fund  or  a  flow. 
A  thousand  shares  in  a  certain  company  owned  by  a  cer- 
tain man  at  a  certain  time  constitute  a  particular  fund  of 
property ;  the  number  of  shares  transferred  in  a  week  on  the 
stock  exchange  constitute  a  flow  of  property.  Again,  the 
value  of  the  checks  held  at  noon  of  any  day  by  one  bank 
drawn  on  other  banks  constitutes  a  fund  of  value ;  the  value 
of  the  checks  which  pass  through  a  clearing-house  in  twenty- 
four  hours  constitutes  a  flow  of  value.  Services  and  satis- 
factions, unlike  wealth  and  property,  can  exist  only  as 
flows;  a  fund  of  either  is  impossible. 

A  fund  is  fully  specified  by  one  magnitude  only;  a  flow 
requires  two,  —  the  amount  of  flow  and  the  duration  of  flow. 
From  these  two  a  third  follows,  —  the  rate  of  flow  or  the 
quotient  of  the  amount  divided  by  the  duration.  The  rate 
of  flow  is  often  of  more  importance  than  the  amount  of  flow. 
Thus  we  care  less  to  know  the  aggregate  wages  of  a  work- 
man during  a  lifetime  than  the  rate  of  his  wages  during 
various  periods  of  his  life. 

The  distinction  between  a  fund  and  a  flow  has  many 
applications  in  economic  science.1  The  most  important  ap- 
plication is  to  differentiate  between  capital  and  income. 
Capital  is  a  fund  and  income  a  flow.  This  difference  be- 
tween capital  and  income  is,  however,  not  the  only  one. 
There  is  another  important  difference,  namely,  that  capital 
is  wealth,  and  income  is  the  service  of  wealth.  We  have 
therefore  the  following  definitions :  A  stock  of  wealth  ex- 
isting at  an  instant  of  time  is  called  capital.  A  flow  of  serv- 
ices through  a  period  of  time  is  called  income.  Thus,  a 
dwelling  house  now  existing  is  capital ;  the  shelter  it  affords 
or  the  bringing  in  of  a  money-rent  is  its  income. 

1  For  some  of  these  applications,  e.g.  to  monetary  circulation,  see : 
"  What  is  Capital  ?  "  Economic  Journal,  1897. 


SEC.  2]  CAPITAL  53 

The  railways  of  the  country  are  capital ;  their  services  of 
transportation  or  the  dividends  from  the  sale  of  that 
transportation  are  the  income  they  yield. 

The  distinction  between  capital  and  income  is  somewhat 
analogous  to  the  distinction  between  desirability  and  satis- 
factions, which  was  emphasized  in  Chapter  III ;  for  desira- 
bility was  shown  to  relate  to  a  point  of  time  and  satisfactions 
to  a  period  of  time. 

§2 

The  foregoing  definitions  of  capital  and  income  are  not, 
it  is  true,  universally  accepted.  Many  authors  attempt 
to  define  capital,  not  as  wealth  in  a  particular  as- 
pect with  reference  to  time,  but  as  a  particular  kind  or 
species  of  wealth,  or  as  wealth  restricted  to  a  particular 
purpose;  in  short,  as  some  specific  part  of  wealth  instead 
of  any  or  all  of  it.  We  are  obliged,  therefore,  to  pause  a 
moment  to  consider  these  opinions.  In  this  chapter 
we  are  concerned  with  the  concept  of  capital  only. 

From  the  time  of  Adam  Smith  it  has  been  asserted 
by  economists,  though  not  usually  by  business  men, 
that  only  particular  kinds  of  wealth  could  be  capital,  and 
the  burning  question  has  been,  What  kinds  ?  But  the  fail- 
ure to  agree  on  any  dividing  line  between  wealth  which  is 
and  wealth  which  is  not  capital,  after  a  century  and  a  half 
of  discussion,  certainly  suggests  the  suspicion  that  no 
such  line  exists.1  What  Senior  wrote  seven  decades  ago 
is  true  to-day:  "Capital  has  been  so  variously  defined, 
that  it  may  be  doubtful  whether  it  have  any  generally 
received  meaning."2  In  consequence,  "almost  every 
year  there  appears  some  new  attempt  to  settle  the  disputed 
conception,  but,  unfortunately,  no  authoritative  result 
has  as  yet  followed  these  attempts.  On  the  contrary, 

1  For  a   fuller   statement    than    that   which   follows   of   the   dis- 
agreements and  confusions  on  this  subject,  see  the  writer's  "What  is 
Capital?"  Economic  Journal,  December,   1896. 

2  "Political  Economy.'1  Encyclopedia  Metropolitana,  Vol.  VI,  p.  153. 


54  NATURE   OF   CAPITAL   AND   INCOME  [CHAP.  IV 

many  of  them  only  served  to  put  more  combatants  in  the 
field  and  furnish  more  matter  to  the  dispute."1  Many 
authors  express  dissatisfaction  with  their  own  treatment 
of  capital,  and  even  recast  it  in  successive  editions.2 

Adam  Smith's 3  concept  of  capital  is  wealth  which 
yields  "revenue."  He  would  therefore  exclude  a  dwelling 
occupied  by  the  owner.  Hermann/  on  the  other  hand, 
includes  dwellings,  on  the  ground  that  they  are  durable 
goods.  But  a  fruiterer's  stock  in  trade,  which  is  capital 
according  to  Smith,  because  used  for  profit,  according  to 
Hermann  does  not  seem  to  be  capital,  because  it  is  perish- 
able. Knies  5  calls  capital  any  wealth,  whether  durable  or 
not,  so  long  as  it  is  reserved  for  future  use.  Walras 6 
attempts  to  settle  the  question  of  durability  or  futurity 
by  counting  the  uses.  Any  wealth  which  serves  more  than 
one  use  is  capital.  A  can  of  preserved  fruit  is  therefore 
capital  to  Knies  if  stored  away  for  the  future,  but  is  not 
capital  to  Walras  because  it  will  perish  by  a  single  use. 
To  Kleinwachter,7  capital  consists  only  of  "tools"  of  pro- 
duction, such  as  railways.  He  excludes  food,  for  instance, 
as  passive.  Jevons,8  on  the  contrary,  makes  food  the  most 
typical  capital  of  all,  and  excludes  railways,  except  as  rep- 
resenting the  food  and  sustenance  of  the  laborers  who  built 
them. 

While  most  authors  make  the  distinction  between  capital 
and  non-capital  depend  on  the  kind  of  wealth,  objectively 
considered,  Mill 9  makes  it  depend  on  the  intention  in  the 
mind  of  the  capitalist  as  to  how  he  shall  use  his  wealth, 

1  Bohm-Bawerk,  Positive  Theory  of  Capital,  English  translation, 
London  and  Now  York,  1891,  p.  23. 

•  E.g.  Roscher,  Marshall,  Schaffle. 

3  Wealth  of  Nations,  Book  II,  Chap.  I. 

4  Staaiswirtschaftliche  Untcrsuchungcn,  Munich,  1832,'  p.  59. 

6  Dux  f it-Id,  2d  od.,  Berlin,  1885,  pp.  69-70. 

*  Elements  d' Economic  Politique  Pure,  4th  ed.,  Lausanne,  p.  177. 

7  Grundlagen  dcx  Xorialismus,  1885,  p.  184. 

8  Theory  of  Politic,,!  Economy,  3d  ed.,  1888,  Chap.  VII,  pp.  222,  242. 
8  Principle*  of  Political  Economy,  Book  I,  Chap.  IV,  §  1. 


SEC.  2]  CAPITAL  55 

Marx  l  makes  it  depend  on  the  effect  of  the  wealth  on  the 
laborer,  and  Tuttle,2  upon  the  amount  of  wealth  possessed. 
Again,  while  most  authors  confine  the  concept  of  capital 
to  material  goods,  MacLeod3  extends  it  to  all  immaterial 
goods  which  produce  profit,  including  workmen's  labor, 
credit,  and  what  he  styles  "incorporeal  estates,"  such  as 
the  Law,  the  Church,  Literature,  Art,  Education,  an  au- 
thor's Mind.  Clark4  takes  what  he  styles  "pure"  capital 
out  of  the  material  realm  entirely,  making  it  consist,  not 
of  things,  but  of  their  utility.  Most  authors  leave  no  place, 
in  their  concept  of  capital,  for  the  value  of  goods  as  distinct 
from  the  concrete  goods  themselves,  whereas  Fetter,5  in  his 
definition,  leaves  place  for  nothing  else.  Some  definitions 
are  framed  with  especial  reference  to  particular  problems 
of  capital ;  many,  for  instance,  have  reference  to  the  prob- 
lem of  capital  and  labor,  but  they  fail  to  agree  as  to  the  re- 
lation of  capital  to  that  problem.  MacCulloch  6  regards  it 
as  a  means  of  supporting  laborers  by  a  wage  fund;  Marx,1 
as  a  means  of  humiliating  and  exploiting  them;  Ricardo,7 
as  a  labor  saver;  MacLeod,3  as  including  labor  itself  as 
a  special  form  of  capital. 

Many  definitions  have  reference  to  the  problem  of 
production,  but  in  no  less  discordant  ways.  Accord- 
ing to  Senior,8  Mill,9  and  many  others,  capital  must  be 
itself  a  product.  Walras,10  MacLeod,3  and  others  admit 

1  Capital,  English  translation,  London,  1887,  Vol.  II,  p.  792. 

2  "The  Real  Capital  Concept,"  Quarterly  Journal  of  Economics 
November,  1903. 

3  Dictionary  of  Political  Economy,  article  "Capital,"  p.  331. 

4  Capital  and   its  Earnings,   Publications  of  American  Economic 
Association,  1888,  pp.  11-13. 

5  "Recent  Discussion  of  the  Capital  Concept,"  Quarterly  Journal  of 
Economics,  November,  1900,  and  Principles  of  Economics,  1904. 

6  Principles  of  Political  Economy,  4th  ed.,  p.  100. 

7  Principles  of  Political  Economy,  §  37. 

8  "Political  Economy,"  Encyclopaedia  Metropolitana,  Vol.  VI,  p. 
153. 

9  Principles  of  Political  Economy,  Book  I,  Chap.  IV,  §  1. 

10  Clements  a" Economic  Politique  Pure,  Lausanne,  4th  ed.,  p.  177. 


56  NATURE    OF   CAPITAL   AND   INCOME  [CaAP.  IV 

land1  and  all  natural  agents  under  capital.  Bohm-Bawerk,2 
while  agreeing  that  it  must  be  a  product,  insists  that  it 
must  not  apply  to  a  finished  product.  Marx  3  denies  that 
capital  is  productive.  Bohm-Bawerk  4  admits  that  it  is 
not  "independently"  productive,  but  denies  the  Marxian 
corollary  that  it  should  not  receive  interest.  Other  writers 
make  it  coordinate  with  land  and  labor  as  a  productive 
element. 

As  to  wrhat  it  is  that  capital  produces  there  is  further 
disagreement.  Adam  Smith  5  affirms  that  capital  produces 
"revenue,"  Senior,6  that  it  produces  "wealth."  Others 
vaguely  imply  that  it  produces  value,  services,  or  utility. 

Most  of  the  definitions  involve  some  reference  to  time, 
but  in  many  different  ways.  Hermann  7  has  in  mind  the 
time  the  wealth  will  last;  Clark,8  the  permanency  of  the 
fund  capital  as  contrasted  with  the  transit oriness  of  its 

1  The  fancied  distinction  between  land  and  capital,  viz.,  that  the 
former  yields  rent  and  the  latter  interest,  and  that  rent  varies  with 
different  grades  of  land  whereas  interest  is  uniform  for  all  sorts  of 
capital,  is  based  on  a  confusion  between  quantity  and  value  of  wealth. 
The  return  from  land  per  acre  will,  it  is  true,. vary  according  to  the 
quality  of  the  land.     But  so  also  the  return  from  machinery  of  differ- 
ent grades  will  vary  per  machine.     The  return  from  different  kinds  of 
capital  per  §100  worth  will,  it  is  true,  be  uniform;    but  so  will  the 
return  from  land  per  8100  worth.     For  a  full  treatment  of  this  confu- 
sion see  Fetter's  "The  Relations  between  Rent  and  Interest,"  a  paper 
presented  before  the  American  Economic  Association,  December,  1903. 
Cf.  Clark,  Capital  and  its  Earnings,  p.  27,  and  Distribution  of  Wealth 
(Macmillan,  1899),  Chaps.  IX  and  XIII.     Cannan  developed  the  same 
idea  in  "What  is  Capital?"  Economic  Journal,  June,  1897.     Cf.  the 
writer's  "  R61e  of  Capital,"  Economic  Journal,  December, 1897,  pp.  524, 
526. 

2  Positive  Theory  of  Capital,  English  translation,  London  and  New 
York,  1S91,  p.  38. 

3  Capital,  English  translation,  London,  1887,  Vol.  II,  p.  792. 

4  Cnjiital  find  Interest,  Book  VI. 

'-  Wealth  of  \ations,  Book  II,  Chap.  I. 

""Political  Economy,"  Encyclopaedia  M  etropolitana,  Vol.  VI,  p. 
153. 

7  Staatswirtschaftliche   Untcrsuchungen,  Munich,   1832,  p.  59. 

8  Capital   and   its    Earnings,   Publications   of   American  Economic 
Association,   1XSS,  pp.   11-13. 


SBC.  3]  CAPITAL  £7 

elements,  "capital  goods";  Knies,1  the  futurity  of  satis- 
factions; Jevons,2  and  Landry,3  specifically  the  time  be- 
tween the  "investment"  of  the  capital  and  its  return. 

§3 

It  is  idle  to  attempt  any  reconciliation  between  concepts 
of  capital  so  conflicting,  and  yet  there  are  elements  of 
truth  in  all.  Though  generally  wrongly  and  narrowly 
interpreted,  there  are  certain  recurrent  ideas  which  are 
entirely  correct.  The  definitions  concur  in  striving  to  ex- 
press the  important  facts  that  capital  is  productive,  that  it 
is  antithetical  to  income,  that  it  is  a  provision  for  the  future, 
or  that  it  is  a  reserve.  But  they  assume  that  only  a  part  of 
all  wealth  can  conform  to  these  conditions.  To  the  authors 
of  the  definitions  quoted,  it  would  seem  absurd  to  include  all 
wealth  as  capital,  as  there  would  be  nothing  left  with  which 
to  contrast  it  and  by  which  to  define  it.  And  yet,  as 
Professor  Marshall  says,  when  one  attempts  to  draw  a 
hard-and-fast  line  between  wealth  wrhich  is  capital  and 
wealth  which  is  not  capital,  he  finds  himself  "on  an  in- 
clined plane,"  constantly  tending,  by  being  more  liberal 
in  his  interpretation  of  terms,  to  include  more  and  more  in 
the  term  capital,  until  there  is  little  or  nothing  left  outside 
of  it.  We  are  told,  for  instance,  that  capital  is  "wealth 
for  future  use."  But  "future"  is  an  elastic  term.  As  was 
shown  in  Chapter  II,  all  wealth  is,  strictly  speaking,  for 
future  use.  It  is  impossible  to  push  back  its  use  into  the 
past;  neither  is  it  possible  to  confine  it  to  the  present. 
The  present  is  but  an  instant  of  time,  and  all  use  of  wealth 
requires  some  duration  of  time.  A  plateful  of  food,  how- 
ever hurriedly  it  is  being  eaten,  is  still  for  future  use,  though 
the  future  is  but  the  next  few  seconds;  and  if  by  "future" 
we  mean  to  exclude  the  "immediate  future,"  where  is  the 

1  Das  Geld.  2d  ed.,  1885,  pp.  69-70. 

2  Theory  of  Political  Economy,  3d  ed.,  1888,  Chap.  VII,  pp.  222-242. 

3  L'Interet  du  Capital,  Paris '(Giard),  1904,  p.  16. 


58  NATURE    OF   CAPITAL   AND    INCOME  [CiiAP.  IV 

line  to  be  drawn  ?     Are  we  to  say,  for  instance,  that  capital 
is  that  wealth  whose  use  extends  beyond  seventeen  days  ? 

And  as  all  wealth  is  for  future  use  it  is  also,  by  the  same 
token,  all  a  "  reserve."  To  call  capital  a  reserve  does  not, 
therefore,  in  strictness,  delimit  it  from  other  wealth.  Even 
a  beggar's  crust  in  his  pocket  will  tide  him  over  a  few  hours.1 

Equally  futile  is  any  attempt  definitely  to  mark  off 
capital  as  that  wealth  which  is  "productive."  We  have 
seen  that  all  wealth  is  productive  in  the  sense  that  it  yields 
services.  There  was  a  time  when  the  question  was  hotly 
debated  what  labor  was  productive  and  what  unproductive. 
The  distinction  was  barren  and  came  to  be  so  recognized. 
Xo  one  now  objects  to  calling  all  labor  productive.  And 
if  this  productivity  is  common  to  all  labor,  it  is  equally 
common  to  all  wealth.  If  we  admit  that  a  private  coach- 
man is  a  productive  worker,  how  can  we  deny  that  the 
horse  and  carriage  are  also  productive,  especially  as  the 
three  merely  cooperate  in  rendering  the  very  same  service, 
-  transportation  ? 

Finally,  we  cannot  distinguish  capital  as  that  wealth 
which  bears  income.  All  wealth  bears  income,  for  income 
consists  simply  of  the  services  of  wealth.  But  the  idea 
that  some  wealth  bears  income  and  some  not  has  been  per- 
sistent from  the  time  of  Adam  Smith,  who,  meaning  by  in- 
come only  money  income,  conceived  capital  as  the  wealth 
which  produces  income  in  this  sense,  as  distinguished  from 
the  wealth,  such  as  dwellings,  equipages,  clothing,  and  food, 
which  dissipates  that  income.  A  home,  according  to  him, 
is  not  a  source  of  income,  but  of  expense,  and  therefore  can- 
not be  capital. 

§4 

In  these  and  other  ways  have  economists  introduced,  in 
place  of  the  fundamental  distinctions  between  fund  and  flow, 
and  between  wealth  and  services,  the  merely  relative  dis- 

1  See  the  writer's  "Precedents  for  Defining  Capital,"  Quarterly 
Journal  of  Economics,  May,  1904,  p.  404. 


SEC.  4]  CAPITAL  59 

tinction  between  one  kind  of  wealth  and  another.  As  a 
consequence,  their  studies  of  the  problems  of  capital  have 
been  full  of  confusion.  Among  the  many  confusions 1 
which  have  come  from  overlooking  the  time  distinction 
between  a  stock  and  a  flow  was  the  famous  wage  fund 
theory,  that  the  rate  of  wages  varies  inversely  with  the 
amount  of  capital  in  the  supposed  "wage  fund."  Mac- 
Culloch  wrote : 2  - 

"  To  illustrate  this  principle,  let  us  suppose  that  the  capital  of  a 
country  appropriated  to  the  payment  of  wages  would,  if  reduced  to 
the  standard  of  wheat,  form  a  mass  of  10,000,000  quarters;  if  the 
number  of  laborers  in  that  country  were  two  millions,  it  is  evident 
that  the  wages  of  each,  reducing  them  all  to  the  same  common 
standard,  would  be  five  quarters." 

"The  wages  would  be  five  quarters"  -thus  MacCul- 
loch  —  but  five  quarters  in  what  time  ?  Five  quarters  per 
hour,  per  day,  or  per  year  ?  Divorced  as  it  is  from  any  time 
concept,  this  definition  is  meaningless. 

Even  so  acute  a  writer  as  John  Stuart  Mill  unhesitatingly 
states : 3  — 

"Wages,  then,  depend  mainly  upon  the  demand  and  supply  of 
labour;  or,  as  it  is  often  expressed,  on  the  proportion  between  popu- 
lation and  capital.  By  population  is  here  meant  the  number  only 
of  the  labouring  class,  or  rather  of  those  who  work  for  hire;  and  by 
capital,  only  circulating  capital,  and  not  even  the  whole  of  that,  but 
the  part  which  is  expended  in  the  direct  purchase  of  labour.  To  this, 
however,  must  be  added  all  funds  which,  without  forming  a  part  of 
capital,  are  paid  in  exchange  for  labour,  such  as  the  wages  of  soldiers, 
domestic  servants,  and  all  other  unproductive  labourers.  .  .  .  With 
these  limitations  of  the  terms,  wages  not  only  depend  upon  the  rela- 
tive amount  of  capital  and  population,  but  cannot  under  the  rule  of 
competition  be  affected  by  anything  else.  Wages  (meaning,  of  course, 
the  general  rate  [sic]).  .  .  ." 

A  little  attention  to  business  bookkeeping  would  have 
saved  economists  from  such  errors ;  for  the  keeping  of  rec- 
ords in  business  involves  a  practical  if  unconscious  recog- 

1  See  "What  is  Capital?"  loc.  cit. 

2  Principles  of  Political  Economy,  1st  ed.,  pp.  327-32S,  2d  ed.,  pp. 
377-378.     See  Cannan,  History  of  Theories  of  Production  and  Distri- 
bution, p.  264. 

3  Political  Economy,  Book  II,  Chap.  XI,  §  1. 


60  NATURE    OF   CAPITAL   AND   INCOME          [CnAP.'lV 

nition  of  the  time  principle  here  propounded.  The  "capi- 
tal account"  of  a  railway,  for  instance,  gives  the  condition 
of  the  railway  at  a  particular  instant  of  time,  and  the  "in- 
come account"  gives  its  operation  through  a  period  of  time. 

§5 

It  has  been  objected  that  the  proposed  definition  does 
not  conform  to  established  usage.  So  far  as  economic  prece- 
dent is  concerned,  we  have  already  seen  that  there  is  no 
established  usage.1  Moreover,  in  the  immense  literature 
on  the  subject  there  is  no  lack  of  precedent  for  the  defini- 
tion here  proposed.  Turgot 2  employed  the  term  capital 
in  practically  the  sense  of  a  stock  of  wealth.  J.  B.  Say,3 
Courcelle-Seneuil,4  and  Guyot 5  followed.  Edwin  Cannan,6 
among  present  economists,  reintroduced  it,  and  in  a  very 
clear  and  explicit  way.  To-day  it  is  used  in  five  or  six 
standard  works,7  as  well  as  in  some  minor  writings.  Many 
economists  have  orally  expressed  their  approval  of  the  pro- 
posed definition. 

Others  virtually  or  approximately  adopt  it,  as,  for  in- 
stance, Knies,8  Clark,8  Pareto,8  Giffen,9  De  Foville,10  Flux,11 

1  For  a  fuller  statement  of  this  fact  see  the  writer's  "Precedents 
for  Defining  Capital,"  Quarterly  Journal  of  Economics,  May,  1904. 

2  Formation  and  Distribution  of  Riches,  §  58,  Ashley's  translation 
(Macmillan,  New  York),  pp.  50-59. 

3  See  Tuttle,  "The  Real  Capital  Concept,"  Quarterly  Journal  of 
Economics,  November,  1903,  p.  83;    but   cf.  Bohm-Bawerk,  Positive 
Theory,  English  translation,  p.  59,  n. 

4  Traite  thforique  et  pratique  d'  Economic  Politique,  1867,  tome  I,  p.  47. 

5  Principles  of  Social  Economy,  English  translation,  p.  50. 

6  Theories  of  Production  and  Distribution,  London,  1894,  p.  14. 

7  Among  them  are  Cannan's  History  of   Theories  of  Distribution, 
Hadley's   Economics,  Smart's   Distribution  of   Income,   Daniels's   Fi- 
nance, Fetter's  Principles  of  Economics,  Scligman's  Principles  of  Eco- 
nomics. 

8  See  "What  is  Capital?"  loc.  cit. 
*  In  his  Growth  of  Capital. 

10  In  his  "Wealth  of  France  and  of  Other  Countries,"  English 
translation,  Journal  of  the  Royal  Statistical  Society,  1894. 

"  Economic  Princi/tlfx,  London  (Methuen),  1904,  pp.  16-18. 


SEC.  6]  CAPITAL  61 

Nicholson,1  Hicks,2  and  the  "Committee  [of  the  British 
Association  for  the  Advancement  of  Science]  on  a  Common 
Measure  of  Value  in  Direct  Taxation."  3  Professor  Mar- 
shall says  that  in  earlier  years  he  "invariably  thought  of 
capital  as  the  whole  stock  of  godds,  and  of  interest  as  the 
whole  of  the  usance  or  benefits  derived  from  the  use  of  that 
stock1';4  that  "when  one  approaches  the  problem  of  dis- 
tribution from  the  mathematical  point  of  view,  there  is 
practically  no  choice"  5  but  to  do  so;  and  that  "wealth  in 
the  form  of  houses  or  private  carriages  helped  to  give  em- 
ployment to  labour  as  much  as  when  in  the  form  of  hotels 
or  cabs."  6  He  expressly  concedes  what  is  really  the  chief 
contention  of  the  present  writer  when  he  says:  "I  concur 
in  his  [my]  conclusion  that  whatever  we  do  with  the  word 
capital,  we  cannot  solve  problems  of  capital  by  classifying 
wealth."  7  Yet  he  concludes,  "not  without  doubt,  that  it 
is  best  to"  8  base  his  definition  of  capital  on  such  a  classi- 
fication, purely  out  of  deference  to  what  he  conceives  to  be 
the  dominant  usage. 

§6 

As  to  popular  and  business  usage,  it  may  be  said  that  a 
careful  study  of  this  usage  as  reflected  by  lexicographers, 
who  have  sought  from  time  to  time  to  record  it,9  reveals 
the  fact  that  before  the  time  of  Adam  Smith  capital  was 
not  regarded  as  a  part  of  the  stock  of  wealth,  but  as  synony- 
mous with  that  stock.10  Sometimes  the  inclusion  of  all 

1  In  his  Elements,  pp.  42,  43. 

2  Lectures  on  Economics,  Cincinnati,  1901,  pp.  91,  244. 

3  Report  of  British  Association  for  Advancement  of  Science,  1878, 
Dublin,  p.  220. 

4  "Distribution  and  Exchange,"  Economic  Journal,  1898,  p.  56. 

5  Ibid.  p.  55.       6  Ibid.  p.  57.     7  Ibid.  p.  50.     8  Ibid.  p.  56. 

9  See  the  writer's  "Precedents  for  Defining  Capital,"  loc.  cit.,  where 
are  presented  the  results  of  an  examination  of  seventy-two  diction- 
aries. 

10  Originally. the  term  "capital"  was  not  a  noun, but  an  adjective. 
"  Capitalis  pars  debiti  "  indicated  the  principal  part  of  a  debt,  i.e.  the 
"principal  "  as  distinguished  from  the  interest.     This  virtually  repre- 


62  NATURE   OF   CAPITAL   AND   INCOME  [CHAP.  IV 

stock  as  capital  was  explicit,  as,  for  instance,  in  the  year 
1611,  Cotgrave  defined  capital  as,  "wealth,  worth;  a  stocked 
Again,  we  find  :  — 

1678,  Dufresne  du  Cange,  Glossarium.  —  Capitale  dicitur  bonum 
omne  quod  possidetur.  .  .  . 

More  often  capital  is  explained  as  a  term  employed  in 
business,  as :  — 

1759,  Rider,  W.  A  New  Universal  English  Dictionary.  .  .  . 
London.  —  Capital.  Among  merchants,  the  sum  of  money  brought 
in  by  each  party  to  make  up  the  common  stock.  Likewise  the  money 
which  a  merchant  first  brings  into  trade  on  his  own  account. 

Here  the  phrase  "among  merchants"  is  perhaps  intended 
to  specify  the  sphere  in  which  the  term  is  generally  found, 
rather  than  as  a  necessary  limitation  to  that  sphere,  just 
as  "hawser"  is  explained  as  a  "nautical  term"  without 
implying  that  a  hawser  could  not  be  employed  on  shore.1 

With  the  advent  of  the  economists  the  dictionary 
definitions  were  thrown  into  confusion,  although  the  great 
majority  of  them  continue  still  to  adhere  to  the  original 
usage;  e.g.:  — 

1883,  Simmonds,  P.  L.  The  Commercial  Dictionary.  .  .  .  Capital 
.  .  .  the  net  worth  of  a  party. 

1894.  Palgrave's  Dictionary  of  Political  Economy,  under  "Assets." 
The  assets  remaining  after  the  discharge  of  liabilities  are  a  person's 
actual  capital. 

In  many  cases  it  is  thought  necessary  to  distinguish 
between  the  meaning  of  capital  among  economists  and  its 
meaning  among  business  men ;  e.g. :  — 

1893,  Murray,  J.  A.  H.  A  New  English  Dictionary.  .  .  .  Vol.  II, 
Oxford.  —  Capital,  B.  sb.  3.  A  capital  stock  or  fund.  a.  Commerce. 
The  stock  of  a  company,  corporation,  or  individual  with  which  they 
cnlcr  into  business  and  on  which  profits  or  dividends  are  calculated; 

s'Titi'd  tin;  distinction  bclwn.-n  a  lund  and  a  How.  The  term  soon 
became  applied  to  a  merchant's  stock  in  contradistinction  to  the  flow 
of  profits  springing  from  it,  and  hence  to  any  fund  or  stock  what- 
ever. Hoe  "Precedents  for  Defining  Capital,"  Quarterly  Journal  of 
Economic*.  May,  1904,  p.  395. 
1  See  "Precedents,"  pp.  8,  9. 


SEC.  0]  CAPITAL  63 

in  a  joint  stock  company,  it  consists  of  the  total  sum  of  the  contribu- 
tions of  the  shareholders,  b.  Pol.  Econ.  The  accumulated  wealth  of 
an  individual,  company,  or  community,  used  as  a  fund  for  carrying 
on  fresh  production;  wealth  in  any  form  used  to  help  in  producing 
more  wealth. 

In  business  manuals  and  articles  on  practical  account- 
ing we  find  that  capital  is  employed  in  the  sense  of  the 
net  value  of  a  man's  wealth.  Thus  L.  W.  Lafrentz,  speak- 
ing of  the  difference  between  assets  and  liabilities,1  states: 
"The  residue  will  be  the  net  worth  of  the  proprietor  — 
the  capital  of  the  proprietor." 

Inquiry  among  business  men  also  reveals  the  fact  that 
in  business  usage  all  wealth  is  included  in  the  term  "capital." 
It  would  astonish  a  business  man  to  have  an  economist 
strike  out  from  his  assets  as  non-capital  his  raw  materials, 
as  would  Kleinwachter ;  his  perishable  goods,  as  wrould 
Hermann;  his  fuel,  as  would  Walras;  or,  above  all,  his 
land,  as  would  most  of  the  classical  economists.  That  land 
is  capital,  business  men  all  emphatically  declare.  As  the 
manufacturer  would  express  it,  land  is  the  very  first  thing 
into  which  the  "paid-in"  capital  of  a  new  concern  is  con- 
verted. Again,  business  men  maintain  that  the  function 
of  any  given  wealth  has  nothing  to  do  with  its  classification 
as  capital.  It  need  not  be  "for  production"  nor  "for  sus- 
taining laborers,"  nor  for  any  particular  object  whatever. 
The  only  point  on  which  some  of  them  hesitate  is  whether 
or  not  all  articles  in  consumers1  hands  are  capital.  The 
reason  for  this  hesitation  may  possibly  be  found  in  the  cus- 
toms of  bookkeeping.  As  one  business  man  expressed  it, 
"Capital  is  simply  a  bookkeeping  term."  Consequently 
the  business  man  naturally  associates  the  term  with  his 
shop  and  not  his  home,  for  he  keeps  a  balance  sheet  in  the 
former  and  not  in  the  latter ;  but,  once  given  a  balance  sheet, 

1 "  Economic  Aspects  of  Accounting  and  Auditing,"  Journal  of 
Accountancy,  April,  1906,  p.  482.  Cf.  Victor  Branford,  Economics  and 
Accountancy,  London  (Gee  &  Co.),  1901,  and  Charles  E.  Sprague,  The 
Accountancy  of  Investment,  New  York  (Business  Publishing  Co.),  1904, 
p.  12. 


64  NATURE    OF    CAPITAL   AND   INCOME  [CHAP.  IV 

it  does  not  matter  what  purpose  is  behind  it.  A  social 
club,  an  art  gallery,  or  a  hospital  may  have  a  capital. 
In  one  year  a  joint  stock  company  with  capital  stock  was 
proposed  for  the  purpose  of  building  the  yacht  for  defend- 
ing the  America  Cup.  If  a  private  family  should  call  it- 
self a  joint  stock  company  and  draw  up  a  balance  sheet, 
entering  all  its  property,  house,  furniture,  provisions,  etc., 
on  one  side,  with  the  debts  on  the  other,  no  business  man, 
we  imagine,  would  hesitate  to  call  the  balance  of  assets  over 
liabilities,  which  is  the  total  wealth-value  of  the  family, 
by  the  name  "capital."  As  a  business  man  said  to 
the  writer,  "Capital  isn't  a  part  of  wealth,  but  all  a 
man  has  got,  including  his  automobile."  "Is  that  cigar 
in  your  mouth  capital?"  he  was  asked.  "No,"  he  said, 
hesitatingly;  but  this  opinion  he  quickly  reversed  as  in- 
consistent with  his  former  statement,  and  admitted  that  a 
box  of  cigars  and  each  cigar  in  it,  or  out  of  it,  for  that  matter, 
were  a  part  of  his  stock  or  reserve. 

The  phrases  "to  capitalize"  and  "to  live  on  capital," 
as  used  by  business  men,  imply  that  capital  is  simply  a  fund. 
When  we  "capitalize"  an  annuity  of  $5  a  year  at  a 
given  sum,  as  $100,  we  mean  that  $100  is  the  fund  of 
ready-money  equivalent  of  $5  flowing  in  annually.  It  does 
not  matter  what  kind  of  goods  the  $5  of  income  or  the 
$100  of  capital  represents.  Again,  when  we  say  that  a 
man  is  "living  on  capital,"  we  mean  that  he  is  using  up 
his  stock  faster  than  he  is  replacing  it.  The  reference 
is  not  to  any  particular  part  or  kind  of  the  stock.  A 
wealthy  New  Yorker  who  was  recently  forced  to  "live 
on  capital"  did  so  by  selling  his  accumulations  of  art  treas- 
ures; it  would  be  the  same  if  he  had  sold  his  stocks  and 
bonds. 

So  far,  then,  as  popular  and  business  usage  is  concerned, 
we  have  ample  warrant  for  the  definition  of  capital  here 
accepted,  and  no  warrant  whatever  for  the  definitions 
ordinarily  found  in  economic  text-books. 


SEC.  7]  CAPITAL  65 

§7 

Should  economists  continue  to  reject  the  simple  defi- 
nition above  explained,  and  insist  on  restricting  the 
term  capital  to  some  narrower  meaning,  our  only  re- 
course will  be  to  follow  the  example  of  John  Rae,1  and, 
after  defining  capital  as  a  part  of  stock,  quietly  shelve 
the  term  and  proceed  to  the  analysis  of  "stock"  instead.2 
We  shall  then  be  in  the  curious  position  of  acknowledging 
that  the " problems  of  capital' 'are  not  problems  of " capital " 
only,  but  of  stock,  and  shall  have  to  regard  such  common 
phrases  as  "the  interest  on  capital,"  "Tinteret  du  capital,'1 
and  " capitalzins"  as  misnomers.  But  this  or  any  other 
settlement  of  the  difficulty  will  be  welcome  to  all  who  are 
tired  of  the  present  confusion  of  tongues.  A  business  friend 
recently  complained  that  he  was  chiefly  deterred  from  read- 
ing the  books  of  economists  because  they  seemed  to  have  no 
settled  terminology.  It  does  not  so  greatly  matter  what 
name  we  select  by  which  to  call  a  concept.  The  important 
matter  is  to  select  for  consideration  those  concepts  which  are 
fruitful  in  scientific  analysis.  That  the  concept — by  what- 
ever name  we  call  it  —  of  a  stock  of  wealth  at  an  instant  of 
time  is  thus  fruitful  will,  we  believe,  appear  more  plainly 
as  we  proceed  to  apply  it  to  what  have  been  called,  rightly 
or  wrongly,  the  "  problems  of  capital." 

1  Sociological  Theory  of  Capital,  edited  by  Professor  Mixter,  Mac- 
millan,  1905. 

2  It  is  not,  of  course,  denied  that  "  stock  "  falls  into  several  more  or 
less  distinct  groups.     One  classification  has  already  been  given  in  the 
chapter  on  "Wealth,"  and  there  are  many  others.     One  of  the  most 
striking  divisions  of  the  stock  of  wealth  as  it  exists  in  modern  society 
is  between  that  at  home  and  that  in  business.     This  is  the  basis  of 
many  definitions  of  capital,  especially  that  of  Komorzynski  (Credit, 
Innsbruck,  1903,  p.  138).     But  the  distinction  applies  only  to  modern 
and  highly  differentiated  societies.   Like  all  classifications  of  concrete 
things,  it  serves  a  descriptive  purpose  but   does   not   help   analysis. 
It  is  well   known  that  in  science  the  most  general  conceptions  are 
the  most  fruitful.      Professor  J.  Willard  Gibbs,    noted  for  the  gen- 
erality and  simplicity  of  his  methods  in  mathematical  physics,  used 
to  say,  "The  whole  is  simpler  than  its  parts." 

F 


CHAPTER  V 

CAPITAL   ACCOUNTS 
§1 

WE  have  defined  capital  as  a  quantity  of  wealth  existing 
at  an  instant  of  time.  A  full  view  of  capital  would  be 
afforded  by  an  instantaneous  photograph  of  wealth.  This 
would  reveal,  in  addition  to  the  durable  wealth,  a  large 
amount  of  goods  of  rapid  consumption.  It  would  disclose, 
not  the  annual  procession  of  such  goods,  but  the  members 
of  that  procession  that  had  not  yet  been  transmuted  in 
form  or  passed  off  the  stage  of  existence,  however  swiftly 
they  might  be  moving  across  it.  It  would  show  train- 
loads  of  meat,  eggs,  and  milk  in  transit,  cargoes  of  fish, 
spices,  and  sugar,  as  well  as  the  contents  of  private  pantries, 
ice  chests,  and  wine  cellars.  Even  the  supplies  on  the  table 
of  a  man  bolting  his  dinner  would  find  a  place.  So  the 
clothes  in  one's  wardrobe  or  on  one's  back,  the  tobacco  in 
a  smoker's  pouch  or  pipe,  the  oil  in  the  can  or  lamp, 
would  all  be  elements  in  this  flash-light  picture  of  capital. 

Such  a  collection  of  wealth  is,  however,  heterogeneous; 
it  cannot  be  expressed  in  a  single  sum.  We  can  inventory 
the  separate  items,  but  we  cannot  add  them  together. 
They  may,  however,  be  reduced  to  a  homogeneous  mass  by 
considering,  not  their  kinds  and  quantities,  but  their 
values.  And  this  value  of  any  stock  of  wealth  is  also  called 
"capital."  To  distinguish  these  two  senses  of  capital,  we 
call  a  stock,  store,  or  accumulation  of  existing  instruments 
of  wealth,  each  instrument  being  measured  in  its  own  unit, 
capital-instruments,  or  capital-wealth,  and  we  call  the 
value  of  this  stock,  when  all  articles  are  measured  in  a  com- 

00 


SEC.  1]  CAPITAL   ACCOUNTS  G7 

mon  unit,  capital-value.  Similarly,  a  quantum  of  property 
rights  existing  at  any  instant  is  called  capital-property, 
and  its  value,  capital-value.  As  a  general  term  to  include 
both  capital-instruments  and  capital-property,  \ve  may 
employ  capital-goods,  a  term  first  suggested  by  Professor 
Clark/ 

We  have,  then,  a  definite  antithesis  between  capital- 
goods  and  capital-value,  capital-goods  being  measured  in 
various  units  appropriate  to  the  various  goods,  as,  for  in- 
stance, in  bushels  of  wheat,  gallons  of  oil,  acres  of  land, 
shares  of  stock,  and  capital-value  being  measured  in  a 
single  uniform  manner,  as  in  dollars  or  other  convenient 
units  of  value.  The  simple  term  "capital"  is  only  em- 
ployed as  an  abbreviation  of  either  of  the  compound  terms 
"capital-goods"  and  "capital-value."  The  business  man 
ordinarily  uses  the  term  "capital"  in  the  sense  of  capital- 
value,  and  hereafter,  unless  it  is  otherwise  specified,  the 
term  "capital"  will  be  understood  in  this  sense.  In 
adopting  this  nomenclature  we  find  ourselves  in  harmony 
with  Professors  Clark,  Fetter,  Tuttle,  and  others  referred  to 
in  the  preceding  chapter. 

We  are  now  ready  to  consider  the  "capital  accounts" 
employed  in  business.  It  is  strange  that  any  treatment 
of  these  accounts  is  generally  omitted  from  economic 
text-books.  There  seems  to  be  no  systematic  study  of  capi- 
tal accounts  in  any  work  on  political  economy. 

A  capital  account  is  a  statement  of  the  amount  and 
value  of  the  property  of  a  specific  owner  at  any  instant  of 
time.  It  consists  of  two  columns,  —  the  assets  and  the 
liabilities.  The  liabilities  of  an  owner  are  the  debts  and 
other  obligations  owing  to  others;  that  is,  they  are  the 
property-rights  of  others  for  which  such  owner  is  respon- 
sible. The  assets  or  resources  of  the  owner  are  all  his  prop- 
erty-rights, irrespective  of  his  liabilities.  The  assets 
include  both  the  property  which  makes  good  the  liabilities, 
and  the  property,  if  any,  in  excess  of  the  liabilities.  They 


68  NATURE    OF    CAPITAL   AND    INCOME  [CHAP.  V 

also  include,  if  exhaustively  considered,  the  person  of  the 
owner  himself. 

The  owner  may  be  either  an  individual  human  being,  or 
a  collection  of  human  beings,  such  as  a  family,  an  asso- 
ciation, a  joint  stock  company,  a  corporation,  or  a  govern- 
ment. With  respect  to  a  debt  or  liability,  the  person 
who  owes  it  is  the  debtor  and  the  person  owed  is  the 
creditor. 

Every  item  in  a  capital  account  is  an  element  of  the 
owner's  total  capital,  the  assets  being  positive  elements 
and  the  liabilities  being  negative.  Consequently,  the  alge- 
braic sum  of  the  elements  of  capital,  or  the  difference  in 
value  between  the  total  assets  and  the  total  liabilities,  is  the 
net  capital,  or  capital-balance  indicated  in  the  account. 


The  items  in  a  capital  account  are  constantly  changing, 
and  their  value  also,  so  that  when,  after  one  statement  of 
assets  and  liabilities  is  drawn  up,  another  is  constructed  at  a 
point  of  time  six  months  later,  the  balancing  item,  or  net 
capital,  may  have  changed  considerably.  However,  book- 
keepers are  accustomed  to  keep  the  item  "capital"  intact 
from  the  beginning  of  their  account,  and  to  denominate  any 
increase  of  it  as  "surplus"  or  "undivided  profits."  There 
are  several  reasons  for  this.  In  the  first  place,  the  less 
often  the  bookkeeper's  entries  are  altered,  the  simpler  the 
bookkeeping.  Again,  by  stating  separately  the  original 
capital  and  its  later  increase,  the  books  show  at  a  glance 
what  the  history  of  the  company  has  been  as  to  the  accumu- 
lations of  capital.  Finally,  in  the  case  of  joint  stock  com- 
panies, the  capital  is  represented  by  stock  certificates,  the 
engraved  "face  value"  of  which  cannot  conveniently  be 
altered  to  keep  pace  with  changes  in  real  value.  Conse- 
quently it  is  customary  for  bookkeepers  to  maintain  the 
book  value  of  the  "capital''  equal  to  the  face  value  of  the 
certificates. 


SEC.  2]                                  CAPITAL   ACCOUNTS  69 

The  following  two  balance  sheets  will  show  the  accu- 
mulation of  "surplus." 

JANUARY  1,  1900 

Assets  Liabilities 

Plant          $200,000     Debts        $100,000 

Capital 100,000 

$200,000  $200,000 

JANUARY  1,  1901 

Plant,   etc $246,324     Debts        $100,000 

Capital 100,000 

Surplus 46,324 


$246,324  $246,324 

But  not  only  is  the  book  item,  capital,  maintained  intact 
as  long  as  possible,  but  often  the  surplus  also  is  put  in  round 
numbers  and  kept  at  the  same  figure  for  several  succes- 
sive reports.  All  the  smaller  fluctuations  have  an  effect 
simply  on  a  third  item  called  "undivided  profits."  The 
distinction  between  surplus  and  undivided  profits  is  thus 
merely  one  of  degree.  The  three  items  —  capital,  surplus, 
and  undivided  profits  —  together  make  up  the  present  net 
capital.  Of  this,  "capital"  represents  the  original  amount, 
"surplus"  the  earlier  and  larger  accumulations,  and  "un- 
divided profits  "  the  later  and  minor.  The  undivided  profits 
are  more  likely  to  appear  in  dividends,  that  is,  to  become 
divided  profits,  although  this  may  also  happen  to  the  surplus, 
or  even  in  certain  cases  to  the  capital  itself. 

We  see,  then,  that  the  capital  of  a  company,  firm,  or 
person  is  to  be  understood  in  two  senses;  first,  as  the 
item  entered  by  the  bookkeeper  under  that  head,  —  the 
original  capital ;  and,  secondly,  this  sum  plus  surplus  and 
undivided  profits,  —  the  true  net  capital  at  the  instant 
under  consideration. 

Inasmuch  as  the  stock  certificates  were  issued  at  the 
formation  of  the  company  and  cannot  be  perpetually 
changed,  they  ordinarily  correspond  to  the  original  instead 


70  NATURE    OF   CAPITAL   AND   INCOME  [CHAP.  V 

of  to  the  present  capital.  Recapitalization  may  be  ef- 
fected, however,  by  recalling  the  stock  certificates  or  issu- 
ing new  ones.  In  these  ways  the  nominal  or  book  value 
may  be  either  decreased  or  increased.  It  is  sometimes 
scaled  down  because  of  shrinking  assets,  and  often  increased 
because  of  new  subscriptions  or  expanding  assets.  If,  for 
instance,  the  original  capital  was  §100,000,  and  the  present 
capital  (that  is,  including  surplus  and  undivided  profits) 
is  $200,000,  it  would  be  possible,  in  order  that  the  total 
certificates  outstanding  might  become  $200,000,  and  the 
surplus  and  undivided  profits  be  enrolled  as  capital,  to 
issue  free  to  each  stockholder  stock  certificates  of  a  face 
value  equal  to  those  already  held.  In  practice,  how- 
ever, such  a  proceeding  is  very  rare.  Ordinarily  the  stock 
certificates  remain  as  originally,  and  merely  increase  in 
value.  Thus,  if  the  present  capital  is  as  in  the  above 
example,  $200,000,  whereas  the  original  capital  and  the 
outstanding  certificates  amount  to  only  $100,000,  the 
market  value  of  the  shares  will  be  double  the  face  value; 
for  the  stockholders  own  a  total  of  $200,000,  represented 
by  certificates  of  the  face  value  of  $100,000. 

§0 
3 

If,  however,  we  attempt  to  verify  such  a  relation  by 
reference  to  the  company's  books,  we  shall  find  some  dis- 
crepancies in  the  results.  For  instance,  the  Second  National 
Bank  of  New  York  had,  at  a  recent  statement,  a  total 
capital,  surplus,  and  undivided  profits  of  $1,295,952.59,  of 
which  the  original  capital  was  only  $300,000.  We  should 
expect,  therefore,  that  the  stock  certificates,  amounting 
to  $300,000,  would  be  worth  $1,295,952.59,  or,  in  other 
words,  that  each  $100  of  stock  certificates  would  be  worth 
$432.  The  actual  selling  price,  however,  is  found  to  be 
$700.  Again,  the  Fourth  National  Bank  of  New  York 
City  had  a  total  capital,  surplus,  and  undivided  profits  of 
$5,700,000,  of  which  $3,000,000  was  capital.  From  this 


SEC.  3]  CAPITAL   ACCOUNTS  71 

we  should  expect  the  shares  to  sell  at  ^1'^=  100.  The 
actual  selling  price,  however,  is  $240.  Here  are  discrep- 
ancies which  call  for  explanation.  If  a  business  man  were 
called  upon  to  explain  them,  he  would  say  that  book 
values  and  market  values  are  entirely  distinct,  the  latter 
depending  on  estimated  "earning  power."  The  stock  is 
worth  its  "capitalized  earning  power,"  and  its  value 
fluctuates  from  day  to  day  in  response  to  a  thousand 
causes.  This  is  quite  true,  but  it  does  not  constitute  a  dis- 
tinction between  book  values  and  market  values,  for  book 
values  also  represent  estimated  earning  power.  The  book 
valuations  of  the  company's  lands,  buildings, machinery,  etc., 
were  originally  determined  by  their  earning  power;  their 
cost  value  was,  at  the  time  of  purchase,  a  market  estimate 
of  earning  power  as  truly  as  the  market  price  of  stock.  This 
principle  holds  true  of  liabilities  as  well  as  of  assets.  The 
liabilities  are  simply  capitalized  charges,  interest,  rentals, 
and  other  expenses. 

The  meaning  of  the  discrepancy  is,  therefore,  not  that  one 
valuation  depends  on  earning  power  and  the  other  not, 
but  that  there  are  two  estimates,  one  that  of  the  book- 
keeper, which  is  seldom  revised  and  usually  conservative, 
and  the  other  that  of  the  market,  which  is  revised  daily. 
Thus  the  stockholders  of  the  Second  National  Bank  are 
credited  by  their  bookkeeper  with  owning  81,295,952.59, 
whereas  in  reality  the  total  value  of  their  property  is  more 
nearly  $2,100,000.  The  bookkeeper  has  systematically 
undervalued  the  assets  of  the  bank,  and  even  omitted  some 
valuable  assets  altogether,  such  as  good  will.  The  object 
of  a  conservative  business  man  in  keeping  his  books  is  not 
to  give  mathematical  accuracy,  but  to  make  so  conserva- 
tive a  valuation  as  to  be  well  within  the  market,  even  in 
times  of  financial  stress.  He  is  more  interested  in  safety 
than  in  precision,  and  in  maintaining  his  solvency  even  in 
the  face  of  heavy  shrinkage  of  market  values  than  in  meet- 
ing the  requirements  of  ideal  statistics. 


NATURE    OF    CAPITAL    AND    INCOME  [CHAP.  V 


There  are  thus  two  valuations  of  the  capital  of  a  com- 
pany,—  the  bookkeeper's  and  the  market's.  The  latter  is 
apt  to  be  the  truer  of  the  two,  although  it  must  be  remem- 
bered that  each  of  them  is  merely  an  appraisement.  We 
see,  therefore,  that  the  balance  of  a  company's  books  which 
is  so  carefully  worked  out  to  the  last  cent,  and  which  has 
so  imposing  an  appearance  of  accuracy,  may  be  in  reality 
very  wide  of  the  mark. 

§4 

Not  only  is  there  a  discrepancy  between  the  market  esti- 
mate of  the  present  capital  of  a  company  and  the  book- 
keeper's entries,  but  the  original  capital  paid  in  to  the 
company  may  itself  have  been  quite  different  from  the 
nominal  capitalization,  for  the  stock  may  have  been  sold 
below  or  above  par.  We  see,  then,  that  the  "capital"  of  a 
person  or  firm  has  four  separate  meanings :  —  the  nominal 
"capitalization";  the  actual  original  "paid-in  capital"; 
the  present  accumulated  capital,  or  "capital,  surplus,  and 
undivided  profits"  as  given  by  the  bookkeeper;  and  the 
market  estimate  of  the  same,  i.e.  the  "value  of  the  shares." 
These  and  the  other  senses  of  capital  are  given  in  the 
following  scheme,  which  displays  the  various  uses  of  the 
term  "capital." 


Capital  - 


Capital-goods  j  capital-instruments 
I  capital-property 

assets  and  liabilities 
in  general 


.  Capital-value  - 


.  net  capital 


original 
capital 


present 
capital 


f  nominal  capitali- 
zation 

I  actual      paid-up 
[      capital 

'as  recorded  in 
the  company's 
books,  consist- 
ing of  capital, 
surplus,  and  un- 
divided profits 
market  value  of 
the  shares 


SEC.  5]  CAPITAL   ACCOUNTS  73 

§  5 

We  have  seen  that  the  effect  upon  the  balance  sheet  of 
an  increase  in  the  value  of  the  assets  was  to  swell  the  sur- 
plus or  the  undivided  profits.  Reversely,  a  shrinkage  of 
value  tends  to  diminish  those  items.  For  instance,  if  the 
plant  of  a  company  having  a  capital  of  $100,000  and  a 
surplus  of  $50,000  depreciates  to  the  extent  of  $40,000,  the 
effect  on  the  books  will  be  as  follows :  - 

ORIGINAL   BALANCE    SHEET 

Assets  Liabilities 

Plant $200,000.00     Debts        ....     §150,000.00 

Miscellaneous      .     .       101,256.42     Capital      ....       100,000.00 

Surplus      ....         50,000.00 
Undivided  profits  1,256.42 


$301,256.42  $301,256.42 

PRESENT    BALANCE    SHEET 

Assets  Liabilities 

Plant         ....     $160,000.00    Debts        ....  $150,000.00 

Miscellaneous      .     .       101,256.42    Capital      ....  100,000.00 

Surplus     ....  10,000.00 

Undivided  profits  1,256.42 


$261,256.42  $261,256.42 

Here  the  shrinkage  in  the  value  of  the  plant,  as  recorded 
on  the  assets  side,  comes  out  of  the  surplus  as  recorded  on 
the  liabilities  side. 

In  case  the  surplus  and  undivided  profits  have  both 
been  wiped  out,  the  capital  itself  becomes  impaired.  In 
this  case  the  bookkeeper  may  indicate  the  result  by  scaling 
down  the  capitalization.  This  sometimes  occurs  in  banks 
and  trust  companies,  but  not  often  in  ordinary  business.  It 
is  often  avoided  by  making  up  the  deficiencies  through 
assessment  of  stockholders  or  postponement  of  dividends. 
This  is  required  by  law  in  many  cases,  as  in  that  of  insurance 
companies.  Dishonest  concerns,  however,  often  conceal  the 
true  state  of  the  case  by  the  reverse  process  of  exaggerating 


74  NATURE   OF   CAPITAL   AND   INCOME  [CHAP.  V 

the  value  of  the  assets.  Sometimes  this  is  done  systemat- 
ically, as  in  the  case  of  stock-jobbing  concerns.  Unscrupu- 
lous promoters  often  invest  the  sums  entrusted  to  them 
by  confiding  stockholders,  in  unwise  or  fraudulent  ways. 
For  instance,  we  may  imagine  an  Oil  Well  Company  in 
California,  of  the  type  called  "stock-producing  wells," 
which  borrows  $50,000  and  collects  $50,000  more  from  the 
sale  of  stock  (at  par),  and  with  this  $100,000  purchases 
land  of  friends  at  a  fancy  price,  collusively  providing  that 
the  proceeds  be  returned  in  large  part  to  the  promoter. 
In  such  a  case  the  books  of  the  bubble  concern  will  show 
the  following  figures :  - 

Assets  Liabilities 

Land $100,000     Debts $50,000 

Capital 50,000 


$100,000  $100,000 

But  if  the  land  is  worth,  say,  only  $60,000,  these  accounts 
should  read :  — 

Assets  Liabilities 

Land $60,000     Debts $50,000 

Capital 10,000 


$60,000  $60,000 

In  other  words,  the  investor  has  only  $10,000  worth  of 
property,  instead  of  the  $50,000  which  he  put  in,  or  20 
cents  for  every  dollar  he  invested.  The  rest  has  been 
diverted  into  the  pockets  of  the  promoter  and  those  in 
collusion  with  him. 

A  favorite  method  of  concealing  the  real  condition  of  a 
company  is  to  enter  among  the  assets  the  bad  debts  due  it, 
at  their  nominal  value.  Sometimes  bad  debts  are  bought 
up  for  that  special  purpose,  the  fraudulent  company  invest- 
ing in  the  notes  of  some  bankrupt  concern,  which  can  be 
obtained  for  very  little,  but  may  be  entered  on  the  books 
at  face  value.  It  is  clear  that  any  exaggeration  on  the 
assets  side  of  the  ledger  produces  an  equal  exaggeration  of 


SEC.  6]  CAPITAL  ACCOUNTS  75 

the  capital,  surplus,  and  undivided  profits,  on  the  opposite 
side.  A  great  responsibility,  therefore,  rests  on  those  who 
construct  commercial  accounts. 

§6 

Thus  far  we  have  considered  the  fluctuations  of  the 
items  of  a  capital  account  independently  of  any  payments 
between  the  company  and  the  stockholders.  When  pay- 
ments are  made  to  the  stockholders  in  the  shape  of  divi- 
dends, the  effect  is  to  reduce  both  sides  of  the  account,  de- 
pleting the  cash  on  the  assets  side,  and  the  undivided  profits 
on  the  liabilities  side,  each  by  the  amount  of  the  dividend. 
If  a  dividend  is  declared  larger  than  the  undivided  profits, 
the  effect  will  be  to  reduce  the  surplus,  or  even  the  capital. 
For  most  business  concerns  it  is  regarded  as  bad  policy, 
or  even  fraudulent,  to  pay  dividends  out  of  capital.  How- 
ever, there  is  no  inherent  reason  why  such  dividends 
should  not  be  paid,  and  in  some  sorts  of  business  it  is  not 
only  proper  but  necessary.  In  these  cases  when  divi- 
dends are  paid  out  of  capital  there  should  be  a  corre- 
sponding reduction  in  the  amount  of  outstanding  capital 
stock,  in  order  that  those  dealing  with  the  concern  may  not 
be  deceived.  For  instance,  land  companies  in  Colorado 
and  California,  such  as  the  Redondo  Land  Company,  are 
formed  for  the  express  purpose  of  investing  in  land  and  sell- 
ing it  again.  As  fast  as  it  is  sold,  the  proceeds  are  divided 
among  the  stockholders,  and  stock  certificates  cancelled, 
until  the  whole  capital  of  the  company  is  cleared  away. 
Ordinarily,  however,  reduction  in  capital  takes  other  forms 
than  dividend  payments.  The  payment  of  dividends  out 
of  capital  is,  generally  speaking,  unlawful,  otherwise  the 
creditors  of  a  company  might  suddenly  find  themselves 
without  any  adequate  security  for  their  loans. 

Payments  are,  of  course,  also  made  from  the  stock- 
holders to  the  company.  We  will  suppose  that  a  company 
is  formed  with  a  capital  stock  of  $100.000,  but  that  when  its 


76  NATURE   OF   CAPITAL   AND   INCOME  [Cnxr.  V 

first  statement  is  made  only  $60,000  of  this  stock  has  been 
subscribed.  It  would  be  possible  for  the  bookkeeper  to 
enter  the  capital  at  that  moment  as  $60,000;  but,  follow- 
ing his  rule  of  keeping  the  capital  item  the  same  in  all  suc- 
cessive accounts,  he  will  place  the  whole  $100,000  on  the 
liabilities  side,  and,  to  offset  it,  will  insert  on  the  other  side 
assets  of  $40,000  in  the  form  of  treasury  stock,  the  idea 
being  that  the  company  holds,  in  its  treasury,  stock  cer- 
tificates for  $40,000,  which  are  to  be  regarded  as  an  asset. 
Of  course  this  mode  of  entering  treasury  stock  is  a  book- 
keeping fiction,  for  this  sum  of  $40,000  represents  what 
is  neither  owned  by  nor  owing  to  the  company,  except  in  the 
sense  that  the  company  owes  itself;  yet  promoters  will 
often  impose  upon  the  credulous  investor  the  statement  that 
to  keep  a  certain  amount  of  the  stock  of  the  company  in  its 
own  treasury  increases  by  that  much  the  property  of  the 
stockholders. 

After  the  capital  stock  has  been  fully  paid  in,  it  is  often 
necessary  to  enlarge  it.  Let  us  suppose  that  before  the 
increase  in  capital  the  account  stands  as  follows :  — 

Assets  Liabilities 

Miscellaneous      .     .     .     $300,000     Debts        $100,000 

Capital 100,000 

Surplus  and  undivided 

profits        ....       100,000 


$300,000  $300,000 

Next  let  new  capital  to  the  extent  of  $100,000  be  issued 
and  sold  to  old  stockholders  at  par,  in  lots  proportionate 
to  their  original  holdings.  The  new  stock  certificates  of 
face  value  of  $100,000  are  thus  sold  for  $100,000.  The 
accounts  will  then  stand  as  follows :  — 

Assets  Liabilities 

Miscellaneous      .     .     .     $400,000     Debts        $100,000 

Capital 200,000 

Surplus  and  undivided 

profits        .     .     .     .       100.000 

$400,000  $400,000 


SEC.  7]  CAPITAL    ACCOUNTS  77 

The  additional  capital  will  first  take  the  form  of  cash, 
but  afterward,  by  the  purchase  of  plant,  equipment,  etc., 
will  be  changed  into  these  or  other  forms  of  wealth  or 
property.  We  shall  suppose,  however,  for  the  present,  that 
in  whatever  form  invested,  the  value  remains  exactly  equal 
to  the  cost,  namely,  $100,000,  so  that  the  assets  are 
changed  from  $300,000  to  $400,000. 

§  7 

Let  us  assume  that  the  books  accurately  represent  actual 
values  and  correspond  to  market  prices.  After  the  new  issue 
of  stock,  we  find  $200,000  of  stock  certificates  representing 
$300,000  of  actual  value  of  capital,  surplus  and  undivided 
profits,  or  $150  per  share.  But  the  new  stock  was,  we 
assumed,  issued  to  them  at  $100  a  share.  Hence  the 
original  stockholders  will  be  able  to  make  a  profit  on  their 
new  stock  by  buying  at  the  issue  price  of  $100  and  then 
selling  at  $150 ;  or  they  may  shorten  this  operation  by  sell- 
ing their  "right  to  subscribe"  for  $50.  At  first  sight  it 
would  seem  as  though  this  right  to  subscribe  represented 
a  mysterious  bonus  to  the  stockholders,  due  to  the  issue  of 
the  new  stock.  It  must  be  remembered,  however,  that 
the  $100,000  par  value  of  original  stock  certificates  repre- 
sented, including  the  surplus,  $200,000  worth  of  property 
belonging  to  the  stockholders,  consequently  the  original 
certificates  were  worth  $200  per  share.  That  is,  the  effect 
of  issuing  new  stock  below  the  original  market  price  was 
to  lower  the  value  of  the  old  stock  from  $200  per  share  to 
$150  per  share.  Consequently  the  loss  of  $50  to  the  stock- 
holders on  their  old  stock  will  exactly  compensate  for  the 
$50  of  excess  value  represented  in  the  rights  to  subscribe. 
An  individual  stockholder  owning  10  of  the  original  shares 
will  find  them  worth,  instead  of  $2000,  only  $1500,  that  is, 
he  will  lose  $500.  This  will  equal  the  profit  of  $500  on 
his  10  new  shares  or  the  value  of  his  rights  to  subscribe 
for  them.  The  outside  public  would  be  willing  to  pay 


78  NATURE    OF    CAPITAL    AND    INCOME  [CHAP.  V 

him  $500  for  the  privilege  of  buying  $1500  worth  of  stock 
for  $1000. 

We  thus  see  that  the  price  at  which  the  new  stock  is 
issued  does  not  of  itself  affect  the  balance  due  the  share- 
holders. And  yet  the  price  of  issue  is  not  a  matter 
of  indifference.  The  lower  the  price  of  issue,  the  greater 
the  inducement  to  the  individual  stockholder  to  subscribe, 
or  to  find  some  one  else  to  subscribe  instead,  and  buy  his 
" right."  Neglect  to  subscribe  (or  to  sell  the  right  to  sub- 
scribe) would  then  cause  a  loss.  The  value  of  the  old  shares 
will  be  lowered  in  any  event,  and  in  such  subscription  or 
sale  lies  the  only  means  of  indemnification.  For  these 
reasons,  it  is  usual  for  new  stock  to  be  offered  to  the  original 
stockholders  below  the  market  price. 

The  exact  compensation  between  the  value  of  the  new 
rights  and  the  depreciation  of  the  old  stock  is  seldom  realized 
in  practice,  because  the  company  may  be  in  a  position  to 
invest  the  new  sums  to  advantage,  in  other  words,  to  buy 
assets  which  are  worth  more  than  cost.  In  this  case  there 
may  be  little  or  no  loss  in  the  value  of  the  old  shares.  But 
the  point  emphasized  still  remains  true,  that  the  price 
of  issue  does  not  of  itself  create  additional  capital  value 
through  the  " right  to  subscribe."  Any  increase  of  value 
will  be  due  to  unusual  opportunities  for  investment,  —  to 
economic  causes  and  not  to  mere  bookkeeping  changes. 

Of  course,  it  may  be  true  that  the  very  fact  of  issu- 
ing new  shares  may  of  itself  create  a  different  opinion 
in  the  stock  market  and  influence  prices  there  for  better  or 
worse.  A  low  price  of  issue  may,  for  instance,  make  the 
stock  more  available  for  small  investors,  and  the  conse- 
quent increase  in  the  volume  of  the  stock  on  the  market 
may  make  it,  temporarily  at  least,  a  subject  for  the  specu- 
lation of  pools.  Such  facts,  while  they  modify  the  results, 
do  not  affect  the  principle. 


SEC.  8]  CAPITAL   ACCOUNTS  79 


We  have  considered  two  ways  through  which  the  book- 
value  of  capital,  surplus,  and  divided  profits  may  ex- 
aggerate the  true  condition  of  the  stockholders'  property, 
namely,  through  misfortune  or  the  unforeseen  shrink- 
age of  the  assets,  and  through  misappropriation  of  stock- 
holders' funds,  even  when  stock  had  at  the  outset  been 
issued  at  par.  There  remains  to  be  considered  a  third 
way,  namely,  through  the  issue  of  stock  below  par,  or  for 
services,  patents,  etc.,  at  unduly  high  prices. 

To  illustrate  this  way  of  overvaluing  capital,  or  "  stock- 
watering/'  suppose  a  company  to  be  capitalized  at  $200,000, 
and  that  this  company  issues  at  the  beginning  1000  certifi- 
cates of  the  par  value  of  $100,000,  but  sells  them  for  only  $60 
per  share  actually  paid  into  the  treasury.  Here  is  $60,000 
paid-in  capital,  represented  by  $100,000  face  value  of  stock 
certificates,  leaving  a  margin  of  $40,000  "  water."  Sup- 
pose, further,  that  another  block  of  $100,000  of  the  stock  is 
given  to  an  inventor  for  his  patent,  the  real  value  of  which 
is  only  $10,000.  Finally,  suppose  that  bonds  are  issued 
to  the  extent  of  $300,000,  and  are  floated  at  par.  Then  the 
company  has  received  in  actual  cash  only  $360,000.  Of 
this  sum  only  $60,000  has  been  received  from  the  stock- 
holders. The  patent,  which  has  also  been  contributed  in 
return  for  $100,000  of  stock,  and  which  is  worth  only  one 
tenth  of  that  sum,  makes  the  total  balance  due  the  stock- 
holders $70,000.  But,  the  company  is  capitalized  at 
$200,000.  Consequently  it  will  be  necessary  for  the  book- 
keeper to  exaggerate  the  assets  to  the  extent  of  $130,000. 

He  may  do  this  as  follows :  — 

Assets  Liabilities 

Plant  [cost  $360,000]  .     $400,000    Bonds $300,000 

Patent  [worth  10,000]  .       100.000    Capital 200,000 

$500,000  $500,000 

Here  $90,000  of  the  exaggeration  is  put  under  patent 
and  the  remainder  in  an  overvaluation  of  the  plant.  Many 


80  NATURE    OF    CAPITAL   AND    INCOME  [CHAP.  V 

other  methods  of  stock-watering  are  possible.  A  common 
one  is  to  allow  the  plant  to  run  down;  i.e.  to  fail  to  make 
proper  repairs,  while  retaining  its  old  book  value  in  the 
balance  sheet.  A  railway  may  be  "skinned"  in  this  way, 
by  diverting  to  dividends  what  should  be  paid  to  a  depre- 
ciation account.  This  operation,  however,  is  not  com- 
monly called  stock-watering,  but  mismanagement. 

It  is  sometimes  said  that  stock-watering  is  not  wrong, 
as  long  as  all  the  terms  and  conditions  are  known.  This 
is  much  like  saying  that  lying  is  not  wrong,  provided  every- 
body knows  that  it  is  lying;  for  a  false  balance  sheet 
is  only  one  form  of  a  false  statement,  and,  ordinarily,  a 
false  statement  is  made  with  intent  to  deceive.  The  object 
may  be,  for  instance,  to  mislead  intending  bondholders  by 
making  them  believe  that  there  is  a  larger  security  for  their 
loans  than  actually  exists.  We  see  here  one  reason  why 
honest  men  often  wncfervalue  their  assets.  They  prefer, 
if  there  is  any  error  in  their  valuations,  that  the  error 
shall  be  against  themselves  rather  than  in  their  favor; 
in  other  words,  that  their  representations  as  to  finan- 
cial strength  shall  be  well  within  the  truth.  Yet  it 
not  infrequently  happens  that  undervaluations  of  assets 
may,  like  overvaluations,  serve  the  purposes  of  dishonesty, 
-  to  "bear"  the  speculative  market,  for  instance. 

Many  attempts  have  been  made  to  prevent  the  frauds 
which  result  from  stock-watering.  For  instance,  the  State 
or  National  governments  compel  publicity  of  accounts  in 
the  case  of  insurance  companies,  national  banks,  and  inter- 
state railways.  The  stock  exchanges  require  similar  pub- 
licity in  regard  to  "listed"  securities.  Any  company  whose 
securities  are  listed  on  the  New  York  Stock  Exchange 
must  publish  its  assets  and  liabilities  at  stated  intervals. 
But  this  rule  is  too  general  to  be  very  effective.  In  some 
cases  the  law  requires  the  entire  nominal  capital  to  be  paid 
into  the  company,  in  cash  or  securities  at  their  market 
value,  as  in  the  case  of  national  banks.1 

1  Revised  Statutes,  §  .",140  (Art  June  3,  1804.  §  13). 


SEC.  9]  CAPITAL  ACCOUNTS  81 

§   9 

The  original  capital  of  a  concern  may  therefore  be  either 
increased  or  decreased.  In  the  course  of  its  fluctuations 
it  may  sometimes  shrink  to  zero.  If  it  sinks  below  zero  we 
have  insolvency,  —  the  condition  in  which  assets  fall  short 
of  liabilities.  The  capital-balance  is  intended  to  prevent 
this  very  calamity;  that  is,  it  is  for  the  express  purpose 
of  guaranteeing  the  value  of  the  other  liabilities. 

These  other  liabilities  represent,  for  the  most  part,  fixed 
blocks  of  property  carved  out,  as  it  were,  of  the  assets,  and 
which  the  merchant  or  company  has  agreed  to  keep  intact 
at  all  hazards.  The  fortunes  of  business  will  naturally  cause 
the  whole  volume  of  assets  to  vary  in  value,  but  all  this 
"slack"  ought  properly  to  be  taken  up  or  given  out  by  the 
capital,  surplus,  and  undivided  profits.  Capital  thus  acts  as  a 
buffer  to  keep  the  liabilities  from  overtaking  the  assets.  It  is 
the  "margin"  put  up  by  those  most  interested  in  an  enter- 
prise, as  a  guarantee  to  others  who  advance  their  capital  to  it. 
The  amount  of  capital-balance  necessary  to  make  a  business 
reasonably  safe  will  differ  with  circumstances.  A  capital- 
balance  equal  to  five  per  cent  of  the  liabilities  may,  in  one 
kind  of  business,  such  as  mortgage  companies,  be  perfectly 
adequate,  whereas  fifty  per  cent  may  be  required  in  another 
kind.  Much  depends  on  how  likely  the  assets  are  to  shrink 
and  how  much;  and  much,  likewise,  on  the  character  of  the 
liabilities.  If  the  assets  have  stability  of  value,  less  capital 
will  be  required  than  if  they  consist  of  speculative  securities. 

The  risk  of  insolvency  is,  then,  the  chance  that  the  assets 
may  shrink  below  the  liabilities.  This  risk  is  the  greater, 
the  more  shrinkable  the  assets,  and  the  less  the  margin  of 
capital-value  between  assets  and  liabilities.  The  subject 
lends  itself  to  mathematical  and  statistical  treatment ; 
but  to  work  out  the  quantitative  relations  would  lead  us 
far  afield  ;  it  would  require  much  statistical  material,  and 
its  analysis  bv  the  mathematics  of  chances. 


82  NATURE   OF   CAPITAL   AND   INCOME  [CHAP.  V 

§  10 

Insolvency  may  exist  for  a  time  without  being  known ; 
there  may  be  no  legal  bankruptcy.  Legal  bankruptcy 
exists  as  soon  as  there  is  a  legal  declaration  of  inability 
to  meet  obligations.  This  may  not  be  true  insolvency. 
For  instance,  the  assets  may  exceed  the  liabilities,  but  the 
cash  assets  at  the  particular  time  may  be  less  than  the  cash 
liabilities  due  at  that  time.  This  condition  we  may  call 
pseudo-insolvency.  In  such  a  case,  a  little  forbearance  on 
the  part  of  creditors  may  be  all  that  is  necessary  to  prevent 
financial  shipwreck. 

A  wise  merchant,  however,  will  not  only  avoid  insolvency, 
but  also  pseudo-insolvency;  that  is,  he  will  not  only  keep 
his  assets  in  excess  of  his  liabilities  by  a  safe  margin,  but 
will  also  see  that  his  assets  are  invested  in  the  right  form 
so  as  to  enable  him  to  cancel  each  claim  at  the  time  and 
in  the  manner  agreed  upon. 

From  this  point  of  view  there  are  three  chief  forms  of 
assets,  —  cash  assets,  quick  assets,  and  slow  assets.  A  cash 
asset  is  property  in  actual  money,  or  what  is  acceptable  in 
place  of  money.  A  quick  asset  is  one  which  may  be  ex- 
changed for  cash  in  a  relatively  short  time,  as,  for  instance, 
call  loans,  short-time  loans,  and  other  marketable  securities. 
A  slow  asset  is  one  which  can  be  exchanged  for  cash  only  in  a 
relatively  long  time,  as  real  estate,  office  fixtures,  and  manu- 
facturers' equipment.  The  skill  of  a  good  business  man 
consists  in  properly  marshaling  these  various  constituents 
of  his  assets. 

§  11 

When  we  speak  of  the  assets  falling  short  of  the  liabilities, 
we  refer  only  to  those  assets  which  are  included  in  the 
balance  sheet.  There  may  be,  outside  of  the  company, 
private  means  of  stockholders  adequate  to  meet  the  debts 
of  a  company,  but  unavailable.  In  fact,  in  the  case  of  a 
joint  stock  company,  there  is  express  provision  for  "limited 


SEC.  11]  CAPITAL   ACCOUNTS  83 

liability,"  so  that  the  only  assets  which  can  be  considered 
in  determining  solvency  are  those  on  the  balance  sheet  of 
the  company.  However,  in  some  cases,  as  in  the  case  of 
national  banks,  the  stockholders  are  liable  for  double  the 
amount  of  the  capital.  In  the  case  of  a  partnership,  on 
the  other  hand,  the  partners  are  liable  for  almost  all  of 
their  private  property,  so  that  the  individual  member  of 
the  firm  has  always  to  reckon  w.th  a  contingent  liability 
to  the  creditors  of  the  firm. 

Originally,  before  business  was  separated  from  private 
life,  all  of  a  debtor's  assets,  even  including  his  own  person, 
were  regarded  as  pledged  to  the  payment  of  a  debt.  The 
attitude  of  the  law  and  public  opinion  toward  this  matter 
has  changed  greatly.  Only  a  few  generations  ago  an  in- 
solvent debtor  was  imprisoned,  the  theory  being  that  insol- 
vency was  a  crime.  When  intentional,  or  due  to  gross 
negligence,  it  is;  but  when  due  to  the  ordinary  chances  of 
business  it  is  not.  To  put  a  debtor  in  prison  did  not  of 
course  help  him  to  pay  his  debts.  When  this  practical  point 
was  admitted,  special  bankruptcy  acts  were  passed  to  re- 
lieve insolvency  if  very  widespread,  as  after  a  panic.  Such 
acts  were  at  first  merely  temporary,  and  regarded  as 
justified  only  under  extraordinary  circumstances.  To-day, 
however,  laws  exist  by  which  a  bankrupt  may  be  discharged 
free  of  further  liability,  and  without  the  necessity  of  any 
special  legislation.  The  Ray  Act  in  the  United  States,  under 
which  our  present  system  of  bankruptcy  has  been  worked 
out,  was  passed  as  late  as  1898.  In  some  places,  as  in 
France,  the  older  view  of  limited  liability  still  prevails; 
but  the  English  and  American  system  is  not  only  sounder 
in  practice,  as  shown  by  its  results  in  encouraging  legitimate 
enterprise,  but  is  also  based  on  sounder  theory,  for  it 
recognizes  the  fact  that  the  creditor  is  a  risk-taker.  This 
has  always  been  and  is  necessarily  the  case,  however  much 
the  debtor  may  try  to  safeguard  his  creditors'  interests. 
The  capital  of  a  company  exists,  as  we  have  seen,  for  the 


84  NATURE    OF   CAPITAL   AND   INCOME  [CHAP.  V 

purpose  of  minimizing  this  risk,  but  it  cannot  eliminate  it 
altogether. 

§  12 

The  principle  that  a  creditor  of  a  concern  is  a  risk-taker 
has  two  important  corollaries.  The  first  is  that,  when 
bankruptcy  occurs,  though  the  nominal  liabilities  exceed 
the  assets,  their  actual  value  does  not.  We  may  say  that 
so  far  as  their  actual  value  is  concerned,  the  value  of  the 
liabilities  of  a  company  can  never  be  greater  than  the 
assets,  for  they  derive  their  value  from  these  assets.  A  com- 
pany which  can  pay  only  fifty  cents  on  the  dollar  must  have 
its  obligations  classified  as  "bad  debts,"  worth  only  half 
their  nominal  amount.  This  fact  does  not,  of  course, 
justify  the  intentional  repudiation  of  debts.  Some  states 
of  the  United  States  have,  it  is  true,  attempted  to  reduce 
the  burden  of  their  debt  by  offering  to  buy  up  their 
own  bonds  at  their  market  price,  when  this  price  was 
below  par,  owing  to  a  lack  of  confidence  in  their  ultimate 
redemption.  Such  an  operation  is  evidently  a  species  of 
repudiation. 

On  the  other  hand,  we  must  not  regard  it  as  an  unfor- 
givable sin  for  the  bona  fide  bankrupt  not  to  pay  his  debts 
in  full.  So  long  as  the  creditor  understands  in  advance 
the  nature  of  the  risk  he  is  taking,  he  must  abide  by  the 
result.  Nowadays,  in  the  case  of  investments  in  large 
corporations,  this  is  perfectly  well  understood.  Many 
railroads  have  been  bonded  for  almost  their  entire  cost,  the 
bondholder  realizing  fully  that  he  could  obtain  nothing 
unless  the  road  was  a  success.  This  participation  in  risk 
is  particularly  evident  in  the  case  of  income  bonds,  which 
specifically  pay  interest  only  so  long  as  the  road's  income 
is  adequate. 

The  principle  that  the  true  value  of  the  liabilities  is  derived 
from  the  assets  and  can  never  exceed  them  may  seem  to 
have  an  exception  in  the  case  of  a  person  who  succeeds 
in  borrowing  money  "without  capital."  It  is  clear,  how- 


SEC.  12]  CAPITAL   ACCOUNTS  85 

ever,  that  if  we  employ  the  term  "wealth"  in  its  larger 
sense,  a  person  who  is  really  good  for  his  debt  is  him- 
self assets  to  that  extent.  His  present  value  must  in  the 
estimation1  of  his  creditors  be  at  least  equal  to  the  dis- 
counted value  of  his  debt-paying  power;  otherwise  he 
could  not  borrow.  It  follows  that  his  liability,  being  only 
part  of  the  discounted  value  of  his  debt-paying  power, 
cannot  exceed  his  assets. 

The  second  corollary,  from  the  principle  that  all  securities 
imply  risk,  is  that  the  distinction  between  stockholders 
and  bondholders  is  chiefly  one  of  degree,  and  may  be 
bridged  over  by  intermediate  forms.  Preferred  stock 
and  income  bonds  amount  to  very  nearly  the  same  thing. 
The  preferred  stockholder  is  elevated  above  the  common 
stockholder,  and  resembles  a  bondholder  in  that  he  is  as- 
signed a  certain  fixed  amount  of  the  earnings  before  any 
accrue  to  the  common  stockholder.  The  income  bondholder, 
on  the  other  hand,  is  depressed  below  the  other  bondholders, 
and  resembles  a  stockholder  in  that  he  will  not  be  paid  until 
the  ordinary  bondholders  have  been  satisfied.  The  chief 
remaining  differences  between  these  two  forms  of  security 
are  that  the  stock  confers  voting  power,  while  the  bond 
does  not ;  and  that  the  bond  has  a  due  date  for  final  ex- 
tinguishment, while  the  stock  continues  until  the  company 
is  "wound  up." 

The  distinction  between  the  different  classes  of  creditors 
of  a  concern  is  still  further  swept  away  in  some  cases  where 
there  is  no  capital  stock,  as  in  that  of  a  mutual  insurance 
company.  Here  the  policy  holders,  instead  of  being 
creditors  for  fixed  sums  due  them  from  the  company,  as 
are  the  bondholders  of  a  joint  stock  concern,  themselves 
assume  the  risk  of  the  business  and  also  take  whatever 
chance  there  may  be  of  profit.  They  are,  as  it  were,  both 
stockholders  and  creditors.  In  the  accounts  of  a  mutual 
company  there  will  be  almost  no  outside  creditors.  In 
such  companies,  therefore,  bankruptcy  would  seem  to 


86  NATURE    OF    CAPITAL   AND   INCOME  [CHAP.  V 

be  impossible;  but  as  their  debts  for  death  claims  are 
for  specific  sums,  they  may  be  forced  into  liquidation,  if 
unable  to  obtain  these  sums  by  remitting  dividends  or  by 
assessments. 

§13 

When  bankruptcy  occurs,  the  claims  of  creditors  are 
settled  in  one  of  three  ways:  through  an  agreement  of 
" composition,"  by  which  the  creditor  agrees  to  take 
what  he  can  get  and  excuse  the  debtor  for  the  differ- 
ence; through  an  assignment  by  the  debtor  of  his  assets 
to  his  creditors;  or  through  foreclosure  by  the  holder  of 
some  obligation. 

The  final  result  of  bankruptcy  will  be  either  liquidation, 
by  which  the  business  assets  are  sold  and  distributed  and 
the  business  wound  up ;  or  reorganization,  by  which  the 
business  is  continued  and  the  liabilities  are  entirely  changed 
in  character.  In  the  case  of  companies  with  large  fixed 
capital,  as,  for  instance,  railroads,  reorganization  is  the 
usual  result,  and  the  old  bondholders  often  become  the 
stockholders,  the  old  stockholders  surrendering  their  rights 
altogether.  While  this  reorganization  is  being  effected, 
the  affairs  of  the  company  are  administered  by  a  receiver 
appointed  by  the  bankruptcy  court.  He  calls  in  all  the 
stock  and  bonds,  and  issues  temporary  receiver's  certifi- 
cates. These  in  turn  are  exchanged  for  the  new  securities 
when  ready.  However,  the  bondholder  seldom  wishes  to 
assume  his  right  of  control  and  become  a  stockholder,  and 
is  usually  offered  instead  the  option  of  cash  or  some  new 
security  similar  in  kind  to  that  which  he  held  before,  but 
less  in  amount.  He  is  apt  to  accept  one  of  these  alterna- 
tives, realizing  that  to  foreclose  and  take  possession  is 
likely  to  be  more  troublesome,  and,  in  the  end,  less  advan- 
tageous. Thus  the  losses  of  the  old  company  are  "written 
off,"  and  the  reorganized  company  starts  afresh  with  a  clean 
set  of  books.  The  change  is  simply  a  change  in  the  forms 
of  ownership  of  wealth  and  in  the  individual  owners. 


SEC.  14]  CAPITAL   ACCOUNTS  87 

§14 

The  bankruptcy  of  one  firm  often  causes  the  bank- 
ruptcy of  another.  The  interdependence  between  firms 
may  be  clearly  seen  in  the  following  table,  where  the  liabil- 
ity of  one  person  is  represented  by  the  asset  of  another, 
thus :  — 

PERSON   A 

Assets  Liabilities 

Miscellaneous      .     .     .     $100,000     Note  to  B      ....       $50,000 

Capital .50,000 

$100,000  $100,000 

PERSON  B 
Assets  Liabilities 

A's  note $50,000     Note  to  C  et  al.    .     .     .     $40,000 

Miscellaneous  ....       20,000     Capital 30,000 


$70,000  $70,000 

PERSON  C 

Assets  Liabilities 

Note  of  B $20,000     Bills  to  D  et  al.    .     .     .     310,000 

Miscellaneous  ....       20,000     Capital 30,000 

$40,000  $40,000 

PERSON  D 
Assets  Liabilities 

Due  from  C $5000     Miscellaneous     ....     $9000 

Miscellaneous  4000 


$9000  $9000 

Now  suppose  A  fails,  for  the  reason  that  his  assets  un- 
expectedly shrink  to  $10,000,  that  is,  become  890,000  less 
than  they  were  before.  Then  the  value  of  the  liabilities 
shrinks  $90,000.  This  wipes  out  all  of  A's  capital  of  $50,000, 
and  takes  $40,000  from  the  value  of  the  rest  of  his  liability, 
which  was  a  note  to  B.  B  gets,  therefore,  only  $10,000 
out  of  a  claim  of  $50,000  or  only  20  cents  on  the  dollar. 
In  B's  account  this  note  of  $50,000  must  now  be  scaled 


88  NATURE    OF    CAPITAL   AND    INCOME  [CHAP,  V 

down  as  a  bad  asset  worth  only  $10,000  instead  of 
$50,000 ;  that  is,  B's  assets  shrink  $40,000.  A's  loss  is  thus 
enough  to  wipe  out  all  of  B's  capital  of  $30,000,  and  pare 
down  the  value  of  his  other  liabilities  by  $10,000,  so  that  B 
can  now  pay  only  $30,000  out  of  the  $40,000  he  owes.  In 
other  words,  he  is  able  to  pay  only  75  cents  on  the  dollar. 
Next  comes  C,  who  has  $20,000  invested  in  B's  note.  He 
gets  only  75  cents  on  the  dollar,  so  that  this  asset,  nominally 
worth  $20,000,  is  found  to  be  worth  only  $15,000,  and  his 
loss  is  only  $5000.  This  loss  is  not  enough  to  wipe  out  all 
his  capital,  but  only  reduces  it  from  $30,000  to  $25,000, 
so  that  C  remains  solvent.  Consequently  D,  who  owns  C's 
bills  for  $5000,  will  lose  nothing.  The  force  of  the  catas- 
trophe has  been  spent.  It  ruined  A  and  B  and  injured  C, 
but  stopped  short  of  D. 

From  this  example  we  may  see  that  the  statistics  of 
bankruptcies  are  often  misleading.  Thus,  it  is  usual  for 
the  statistician  to  sum  up  the  liabilities  of  all  bankrupt 
firms.  But  in  case  the  various  firms  are  connected,  as  in 
the  above  example,  the  total  sum  lost  is  not  as  great  as 
though  the  same  amount  of  bankruptcy  occurred  in  inde- 
pendent firms.  In  the  preceding  example  the  only  loss  is 
$90,000,  all  in  A's  assets.  But  there  would  appear  to  be 
a  loss  of  $90,000  in  A's  account,  one  of  $40,000  in  B's 
account,  and  one  of  $5000  in  C's,  or  $135,000  in  all. 
This  misleading  result  is  evidently  due  to  counting  parts 
of  the  loss  twice  and  three  times. 

Failures  are  sometimes  due  to  a  false  fear  of  calamity, 
a  shock  to  business  confidence.  This  will  cause  a  shrinkage 
of  values  in  several  ways.  For  instance,  it  will  induce 
creditors  to  demand  payment  and  refuse  renewals  of  bills. 
Forced  liquidation  and  contraction  of  credit  are  the  result. 
No  physical  capital  is  destroyed,  but  the  form  of  ownership 
is  violently  disturbed,  and  often  the  management,  being 
transferred  from  stockholders  to  bondholders,  is  turned 
from  competent  to  incompetent  hands.  Above  all,  the 


SEC.  15]  CAPITAL   ACCOUNTS  89 

expectations  of  the  future  are  changed  and  confused. 
Plans  are  given  up,  orders  are  countermanded,  and  trade 
is  stopped.  Assets,  representing  as  they  do  the  value  of 
future  expectations,  suffer  sudden  and  heavy  reductions. 

§15 

Briefly  summarizing  this  chapter  we  may  say  that  a  per- 
son who  has  liabilities  is,  in  a  sense,  a  trustee.  He  holds 
more  than  he  owns.  He  holds  all  his  assets;  he  owns 
only  the  margin  between  these  and  his  liabilities.  His 
responsibility  for  the  liabilities  requires  that  he  should 
keep  his  own  margin  of  capital  comparatively  safe.  But 
there  is  always  risk  of  losing  his  margin  and  becoming 
insolvent.  This  risk,  whether  large  or  small,  is  necessarily 
assumed  by  his  creditors,  and  its  existence  should  be 
recognized  in  law  as  well  as  in  business  practice.  The 
record  of  the  relations  which  at  any  time  exist  between 
assets,  liabilities,  and  the  margin  of  capital  separating 
them  constitutes  what  we  have  called  the  "capital  ac- 
counts." 


CHAPTER  VI 

CAPITAL   SUMMATION 
§1 

THE  interdependence  of  the  balance  sheets  of  different 
firms  or  companies  which  has  been  revealed  by  the  com- 
munication of  bankruptcies  exists,  of  course,  irrespec- 
tive of  bankruptcies.  It  exists  wherever  any  item 
enters  two  accounts,  in  one  as  asset  and  in  the  other  as 
liability.  In  fact,  every  liability  item  in  a  balance  sheet 
implies  the  existence  of  an  equal  asset  in  some  other  bal- 
ance sheet,  for  every  debtor  implies  a  creditor.  Conse- 
quently every  negative  term  in  one  balance  sheet  is  offset 
by  a  corresponding  positive  term  in  some  other.  The  con- 
verse, however,  does  not  follow,  namely,  that  every  asset 
implies  a  liability. 

When  we  attempt  to  sum  up  the  items  in  the  bal- 
ance sheets  of  various  persons,  the  positive  and  negative 
elements  may  be  canceled  out  by  pairs  or  couples. 
This  method  of  cancellation  may  be  called  the  method  of 
couples.  Each  debt  or  liability  between  any  two  persons 
whose  accounts  are  included,  being  a  liability  to  one  and 
an  asset  to  the  other,  constitutes  a  couple  or  pair  of  equal 
and  opposite  items.  We  have  already  noted  another  way 
in  which  liabilities  may  be  canceled  against  assets,  namely, 
by  subtracting  the  liabilities  in  any  capital  account  from 
the  assets  in  the  same  account.  This  method  may  be 
called  the  method  of  balances,  since  for  each  individual 
account  liabilities  are  deducted  from  assets  and  the  net 
balance  is  taken.  Both  methods  must,  of  course,  lead  to 
the  same  result. 

90 


SEC.  1] 


CAPITAL    SUMMATION 


91 


The   two  methods  may  he  illustrated   by  the   balance 
sheets  of  three  persons,  say  X,  Y,  and  Z :  - 


PERSON  X 

Assets  Liabilities 

Z's  note  .  .     $  30,OOOA   Mortgage  hold  by  Y 


Residence 
R.R.  shares  . 


Assets 

X's  mortgage     .     . 
Personal  effects 
R.R.  shares  . 


Assets 


70,000 
20,000 


(Capital  balance  . 


$  120,000 

PERSON  Y 

Liabilities 

.    $50,OOOB   Debt  to  Z 

20,000      (Capital  balance  .     . 
10,000 


$80,000 

PERSON  Z 


Liabilities 


Y'sdebt $40,OOOC  Debt  to  X  .     .     . 

Farm 50,000      (Capital  balance  . 

R.R.  bonds  ....       20,000 


$110,000 


$50,000'' 
70,000) 

$  120,000 


$40,000" 
40,000) 

$80,000 


$  30,000" 
80,000) 


$110,000 


The  items  which  appear  twice,  once  as  a  liability  of  one 
man  and  again  as  an  asset  of  another,  are  indicated  by  the 
same  letter.  Thus,  "A"  in  X's  assets  is  matched  by  the 
equal  and  opposite  item  "a"  in  Z's  liabilities.  The  method 
of  couples  thus  consists  simply  in  omitting  these  pairs  of 
items  and  entering  those  which  remain.  These,  in  the  pres- 
ent case,  are  all  assets. 

The  results  of  summing  up  the  capital  accounts  by  the 
two  methods  are  shown  in  the  following  tables:  — 


Method  of  Balances 

X's  capital        ....  870,000 

Y's  capital       ....  40,000 

Z's  capital       ....  80,000 


Method  of  Couples 
Residence        ....     §70,000 
Personal  effects  .      .     .       20,000 

Farm 50,000 

R.R.  shares     .  30.000 


R.R.  bonds 


20,000 


§190,000 


§190,000 


92  NATURE    OF   CAPITAL   AND   INCOME  [CHAP.  VI 

The  totals  are  the  same  by  both  methods,  but  the  method 
of  balances  shows  the  share  of  this  total  capital  which  is 
owned  by  each  individual,  while  the  method  of  couples  shows 
the  various  items  of  capital-goods  of  which  this  total  is  com- 
posed, namely,  residence,  personal  effects,  farm  and  railroad 

shares  and  bonds. 

§<-) 
* 

It  is  well  to  note  here  the  distinction  between  the  ac- 
counting of  real  persons  and  of  fictitious  persons.  For 
a  real  person,  the  assets  may  be  and  usually  are  in  excess 
of  the  liabilities,  and  the  difference  is  the  capital-balance 
of  that  person.  This  capital  is  not  to  be  regarded  as  a 
liability,  but  as  a  balance  or  difference  between  the  lia- 
bilities and  the  assets.  For  a  fictitious  person,  on  the 
other  hand,  as  for  instance  a  corporation  or  partnership, 
the  liabilities  are  always  exactly  equal  to  the  assets; 
for  the  balancing  item  called  capital  is  as  truly  an 
obligation  from  the  fictitious  person  to  the  real  stock- 
holders, as  any  of  the  other  liabilities.  A  fictitious 
person,  in  fact,  is  a  mere  bookkeeping  dummy,  hold- 
ing certain  assets  and  owing  all  of  them  out  again  to 
real  persons.  Bookkeepers,  it  is  true,  apply  the  same 
methods  in  both  cases,  but  they  do  so  by  regarding  the 
accounts  even  of  a  real  person  as  relating  to  a  fictitious 
entity  for  bookkeeping  purposes.  One's  business  self  and 
one's  real  self  are  separated.  Thus  if  X's  business  shows  a 
balance  in  X's  favor  of  $10,000,  he  enters  this  as  a 
liability  item  in  his  business  accounts  and  considers  his 
"business"  as  owing  him  this  sum.  There  is  no  objection 
to  such  a  procedure.  But  we  must  remember  that  when 
we  say  that  "X's  business"  owes  X  $10,000,  we  imply  that 
the  real  X  in  his  own  accounts  holds  a  claim  of  that 
amount  against  his  "business."  In  other  words,  we  are 
compelled,  in  order  to  be  consistent,  to  open  a  separate 
account  for  X  and  carry  forward  the  $10,000  balance 
to  the  opposite  side,  thus  :  - 


SEC.  3]  CAPITAL   SUMMATION  93 

X's  BUSINESS 

Assets  Liabilities 

Miscellaneous        .     .     .     $50,000     Due  to  others     .     .     .     $40,000 

Due  to  X       ....       10,000 


$50,000  $50,000 

X's  Self 
Assets 
Due  from  "X's  business"     .     .     $10,000 

In  the  second  account  there  is  no  counterbalancing 
liability.  For  real  persons,  then,  assets  and  liabilities  are 
not  equal.  If  they  were,  the  summation  of  their  balance 
sheets  would  yield  simply  zero !  If  we  would  avoid  this 
absurdity,  we  must  either  omit  the  capital-balance  from 
the  liabilities  side,  or  if  for  the  moment  we  place  it  there, 
we  must,  as  in  the  above  example,  carry  it  forward  to  the 
opposite  side  of  another  account,  which  amounts  to  the 
same  thing  in  the  end. 

§3 

With  this  preliminary  explanation,  let  us  now  introduce 
into  our  summation  the  capital  accounts  of  the  railroad 
whose  stocks  and  bonds  are  included  among  the  assets  of 
persons  X,  Y,  and  Z.  For  simplicity,  we  shall  suppose  that 
these  three  persons  are  the  only  persons  interested  in  the 
road.  The  balance  sheet  of  the  railroad  company  will 
accordingly  appear  as  follows :  - 

RAILROAD  Co. 
Assets  Liabilities 

Railway $50,000     Bonds   (held  by  Z)  .     .     $20,000 

Capital  stock 

(held  by  X)  $20,000 

(held  by  Y)    10,000       30,000 

$50,000  $50,000 

Now  if  we  combine  this  sheet  with  the  preceding  we 
shall  see  that  its  inclusion  does  not  affect  the  results 


94  NATURE   OF   CAPITAL   AND   INCOME          [CHAP.  VI 

which  were  obtained  by  the  method  of  balances  before 
the  railroad  was  introduced  into  the  discussion.  The 
totals  will  stand  as  follows :  - 

X's  capital  balance $  70,000 

Y's  capital  balance 40,000 

Z's  capital  balance 80,000 

R.R.  Co.'s  capital  balance 000 

$190,000 

When  we  apply  the  method  of  couples,  however,  we 
find  that  the  inclusion  of  the  railway  company's  capi- 
tal account  will  affect  the  items  in  the  final  sum.  The 
stocks  and  bonds,  as  assets  of  X,  Y,  and  Z,  will  now  pair  off 
with  the  corresponding  liabilities  of  the  railroad  company 
and  their  place  will  be  taken  by  the  concrete  railroad  itself, 
as  follows :  — 

METHOD  OF  COUPLES 

Residence $  70,000 

Personal  Effects 20,000 

Farm         50,000 

Railway          50,000 


$190,000 

The  appearance  of  the  capital  inventory  is  thus  changed. 
Formerly,  the  items  of  property-rights  in  it  included  part 
rights,  as  stocks  and  bonds;  now  they  consist  only  of 
complete  property-rights  The  items  still  consist,  strictly 
speaking,  solely  of  property  rights  —  the  right  to  the 
residence,  the  right  to  the  farm,  etc.  But,  since  the 
complete  right  to  any  article  of  wealth  is  best  expressed 
in  terms  of  the  article  of  wealth  itself,  instead  of  the  long 
phrase,  the  "right  to  a  residence,"  we  merely  use 
" residence."  The  property  no  longer  veils  the  wealth 
beneath  it,  and  the  inventory,  which  before  was  called 
an  inventory  of  propers-capital,  is  now  also  an  inventory 
of 


SEC.  3]  CAPITAL   SUMMATION  95 

Such  a  result  is  sure  to  follow  when  we  combine  capital 
accounts,  provided  we  combine  enough  of  them  to  supply, 
for  every  liability  item,  its  counterpart  asset,  and  for 
every  asset  which  has  one,  its  counterpart  liability.  The 
assets  which  have  no  counterparts  are  what  we  have 
called  complete  rights  to  wealth,  or  "fee  simples";  those 
which  have  them  are  the  partial  rights  to  wealth.  The 
reason  is  that  every  article  of  concrete  wealth  is  to  be  re- 
garded as  owned  in  "fee  simple"  by  some  one,  even  if  we 
have  to  set  up  a  fictitious  person  as  dummy  for  that  very 
purpose.  Hence  every  part  right  to  that  wealth  will  nec- 
essarily appear  as  a  liability  on  the  opposite  side  of  that  per- 
son's account,  and  again  as  an  asset  on  the  account  of  some 
other  person.  Thus,  if  two  brothers  own  a  farm  in 
equal  shares,  the  farm  as  a  whole  is  regarded  as  owned 
by  the  partnership  person  called  "Smith  Brothers."  The 
balance  sheet  of  this  fictitious  person  will  show  as  assets 
the  farm  and  as  liabilities  the  "undivided  half-interest"  of 
each  brother,  and  these  same  items  enter  the  individual 
accounts  of  the  brothers  as  assets. 

To  follow  out  capital  summations  thus  requires  the  in- 
clusion of  many  fictitious  persons,  for  it  is  often  only  the 
fictitious  persons  who  hold  the  complete  rights  to  articles 
of  wealth.  Locomotives  and  railway  stations,  for  instance, 
are  owned  by  corporations,  not  individuals.  In  fact,  these 
fictitious  persons  —  partnerships,  corporations,  trusts, 
municipalities,  associations,  and  the  like  —  are  formed 
for  the  express  purpose  of  holding  large  aggregations  of 
concrete  wealth  and  parceling  out  its  ownership  among  a 
larger  number  of  real  persons. 

If,  then,  we  suppose  balance  sheets  so  constructed  as  to 
include  the  whole  world  of  real  and  fictitious  persons, 
with  entries  in  them  for  every  asset  and  liability,  even 
public  parks  and  streets,  household  furniture,  persons 
themselves,  and  other  possessions  not  ordinarily  accounted 
for  in  practice,  it  is  evident  that  we  shall  obtain,  by  the 


96  NATURE   OF   CAPITAL   AND   INCOME  [CHAP.  VI 

method  of  balances,  a  complete  account  of  the  distribution 
of  capital-value  among  real  persons;  and,  by  the  method 
of  couples,  a  complete  list  of  the  articles  of  actual  wealth 
thus  owned.  On  this  list  there  will  be  no  stocks,  bonds, 
mortgages,  notes,  or  other  part  rights,  but  only  land, 
buildings  and  other  land  improvements,  commodities  and 
real  persons.  In  other  words,  we  arrive  again  at  the 
proposition  of  Chapter  III,  that  wealth  underlies  and  cor- 
responds to  property. 

§4 

Among  other  part-rights  in  real  wealth  we  find  what  is 
called  "credit."  There  has  been  much  discussion  as  to  the 
nature  of  credit;  whether,  in  particular,  credit  is  to  be 
regarded  as  a  "part  of  capital."  It  has  been  claimed  that, 
from  the  merchant's  point  of  view,  credit  is  capital  be- 
cause it  enables  a  business  man  to  enlarge  his  business. 
In  this  view  it  is  capital,  though  it  is  borrowed  capital. 
MacLeod  specifically  includes  credit  under  capital.  Pro- 
fessor J.  Shield  Nicholson  says  that  credit  is  a  sort  of 
revenue  capital,1  but  that  "  strictly  and  taking  only 
material  (productive)  capital,  this  would  involve  counting 
the  same  elements  twice  over."  We  see,  from  our  study 
of  capital  accounts,  how  to  avoid  such  double  counting. 
That  part  of  a  man's  so-called  capital  which  is  borrowed 
should  not  enter  his  books  as  his  capital  at  all,  being  but  a 
manifestation  of  the  fact  that  the  total  capital  of  the  com- 
munity which  he  in  part  owns  is  also  owned  in  part  by 
others.  Indeed,  the  phenomenon  of  credit  means  nothing 
more  nor  less  than  a  specific  form  of  divided  ownership 
of  wealth.  Credit  merely  enables  one  man  temporarily 
to  control  more  wealth  or  property  than  he  owns,  that 
is,  some  part  of  the  wealth  or  property  of  others.  This 
occurs  generally  on  the  theory  that  he  can  use  it  to  better 
advantage  than  the  real  owner. 

1  Palgrave's  Dictionary  of  Political  Economy,  Vol.  I,  p.  452. 


SEC.  5]  CAPITAL   SUMMATION  97 

It  is  therefore  a  cardinal  error  to  regard  credit  as  in- 
creasing capital  by  the  amount  of  that  credit.  Indirectly, 
credit  may  result  in  an  increase  of  capital,  through 
stimulating  trade  and  production  and  by  getting  the 
management  of  capital  into  the  right  hands  and  its 
ownership  into  the  most  effective  form;  but  the  amount 
of  any  such  increase  of  capital  thus  indirectly  produced 
bears  no  necessary  relation  to  the  amount  of  the  credit 
itself.  If  capital  is  increased,  the  credit  does  not  constitute 
the  increase,  but  merely  represents  a  part  ownership  in  the 
final  total,  after  all  the  increments  have  been  counted  in. 

§5 

A  great  deal  of  confusion  in  legislation  and  writing  could 
be  avoided  if  the  two  methods  of  summing  up  capital  were 
distinguished  and  their  interrelations  recognized.  In  taxa- 
tion, the  two  methods  are  often  confused.  A  chief  prob- 
lem of  efficient  taxation  is  how  to  tax  all  property  once, 
and  none  of  it  more  than  once.  There  are  two  solutions : 
One  is  to  tax  the  amount  owned  by  each  real  person  in  a 
list  which  expresses  the  method  of  balances ;  this  method 
seeks  out  the  real  owners  or  part  owners  of  wealth.  The 
other  is  to  tax  the  actual  concrete  wealth  in  a  list  which 
expresses  the  method  of  couples ;  this  method  seeks  out  the 
real  wealth  owned.  At  present  the  two  are  much  confused. 
Legislators  too  often  fail  to  perceive  that  under  the  first, 
or  owner-method,  corporations  should  not  be  taxed,  for 
they  are  not  true  owners:  and  that  under  the  second,  or 
wealth-method,  bonds,  stocks,  and  other  part-rights  to 
wealth  should  not  be  taxed,  for  these  are  sufficiently  in- 
cluded when  the  actual  railways  and  other  wealth  are  taxed, 
which  these  securities  represent. 

It  is  not  claimed,  of  course,  that  a  complete  system  of 
taxation  can  be  worked  out  merely  by  choosing  one  of  the 
two  forms  of  taxes  just  indicated.  We  are  here  only  con- 
cerned in  pointing  out  that  the  distinction  between  the 


98  NATURE   OF   CAPITAL  AND   INCOME  [CHAP.  VI 

two  should  be  observed  and  that  where  one  is  applied  the 
other  cannot  also  be  applied  without  duplicating  the  tax. 

The  failure  to  distinguish  clearly  the  methods  of  balances 
and  couples  also  manifests  itself  in  the  form  of  fallacious 
statistics  of  capital.  Statistics  of  railway  capital  have  been 
compiled  in  which  the  value  of  all  railway  property  is  ob- 
tained by  adding  up  the  assets  of  the  railways,  regardless 
of  the  fact  that  many  of  these  assets  consist  in  stocks  and 
bonds  of  other  railways. 

We  should  therefore  distinguish  carefully  the  two  meth- 
ods for  the  summation  of  capital,  —  one  the  method  of 
balances,  which  exhibits  capital  as  owned  by  different  in- 
dividuals, and  the  other  the  method  of  couples,  which 
exhibits  capital  as  consisting  of  different  concrete  instru- 
ments. The  one  relates  to  the  owner,  the  other  to  the 
things  owned.  They  do  not  conflict,  but  present  the  same 
facts  in  different  aspects. 


PART   II.     INCOME 

CHAPTER     VII.  INCOME 

CHAPTER  VIII.  INCOME  ACCOUNTS 

CHAPTER      IX.  INCOME  SUMMATION 

CHAPTER        X.  PSYCHIC  INCOME 


CHAPTER  VII 

INCOME 


INCOME  has  already  been  defined  as  a  flow  through  a 
period  of  time  and  not,  like  capital,  as  a  fund  at  an  instant 
of  time,  and  as  consisting  of  abstract  services  and  not, 
like  capital,  of  concrete  wealth.  The  income  from  any  instru- 
ment is  thus  the  flow  of  services  rendered  by  that 
instrument.  The  income  of  a  community  is  the  total  flow  of 
services  from  all  its  instruments.  The  income  of  an  indi- 
vidual is  the  total  flow  of  services  yielded  to  him  from  his 
property.  Before  attempting  to  elaborate  or  even  to  justify 
this  definition,  we  have  first  to  examine  the  erroneous 
concepts  of  income  now  current.  The  present  chapter  is 
devoted  to  such  an  examination. 

It  is  no  exaggeration  to  say  that  at  present  the  state  of 
economic  opinion  on  this  important  subject  is  deplorably 
confused  and  conflicting.  Many  writers  fail  to  construct 
any  definition  whatever,  either  because  they  find  the  task 
too  difficult,  or  because  they  deem  the  concept  too  obvious 
to  require  definition.  And  those  who  do  set  themselves 
the  task  of  reaching  a  working  concept  of  income  do  not 
find  it  an  easy  one  ;  and  authors  often  confess  dissatisfac- 
tion with  their  own  results. 

The  definitions  which  are  given  are  usually  vague.1 
Their  authors,  often  able  and  distinguished,  and  keenly 
alive  to  the  difficulties  of  the  subject,  seem  to  take  refuge 

1  For  a  collection  of  conflicting  definitions  see  Appendix  to  Chap. 
VII,  §  1. 

101 

\mm 

UOTEItSITT  OF  CALUQWA 
RIVERSIDE 


102  NATURE    OF   CAPITAL  AXD   INCOME         [CHAP.  VII 

in  an  obscure  and  ambiguous  phraseology.1  Were  it  not 
for  an  instinctive  feeling  that  there  exists  a  definite  income- 
concept,  the  repeated  failure  to  formulate  it  might  lead  one 
to  conclude  that  it  is  not  susceptible  of  any  exact  and  rig- 
orous definition,  and  that  the  best  course  is  to  abandon  its 
search  as  futile  Kleinwachter,  who  wrote  a  book  espe- 
cially devoted  to  this  subject,  specifically  takes  this  course. 
He  states  that  there  is  no  useful  concept  of  income.2 
His  idea  is  that,  originally,  merchants  attempted  to  keep  a 
record  of  their  transactions  by  counting  the  money  which 
they  received  and  disbursed,  and  that,  in  consequence  of 
this,  arose  the  "illusory"  notion  that  through  some  such 
record  the  complete  economic  standing  of  an  individual  or 
firm  could  be  expressed.  He  observes,  that  such  a  com- 
plete picture  could  not  be  obtained  by  recording  merely 
the  incomings  and  outgoings  of  money,  but  should 
include  likewise  the  incomings  and  outgoings  of  every  other 
kind  of  wealth.3  A  complete  record,  he  states,  would 
alone  cover  the  required  ground.  So-called  statistics  of  in- 
come are,  he  maintains,  merely  a  makeshift  for  such  a  record.4 
But  why  should  the  possibility  of  a  concept  of  income 
be  rejected  because  it  does  not  reveal  a  "  complete"  picture 
of  an  individual's  economic  condition?  On  the  same  plea 
we  might  also  reject  the  possibility  of  a  concept  of  capital. 

1  E.g.  F.  Y.  Edgeworth,  Palgrave's  Dictionary  of  Political  Economy, 
article,  "Income,"  Vol.  II,  p.  374:  — 

"  Income  may  be  defined  as  the  wealth,  measured  in  money,  which 
is  at  the  disposal  of  an  individual,  or  a  community,  per  year  or  other 
unit  of  time."  (The  italics  are  the  present  writer's.)  This  formula- 
tion is  adopted  by  N.  G.  Pierson,  Principles  of  Economics,  London 
(Macmillan),  1902,  p.  76. 

2  Das  Einkommen  und  seine  Verteilung,  Leipzig,  1896,  p.  11. 

3  Op.  tit.,  p.  14. 

4  The  present  writer    at    one    time  also  expressed    these   doubts 
(Economic  Journal,  December,  1896,  pp.  553,  554).     By  aid  of  the 
criticisms  of  Cannan  and  Edgeworth,  the  conclusions  here  stated  were 
reachr-d.     These  were  first  outlined  in  "Senses  of  Capital,"  Economic 
Journal,  June,    1897,   and   in    "  The    R61e   of   Capital    in  Economic 
Th'.-ory,"  Economic  Journal,  December,  1897. 


SEC.  2]  INCOME  103 

A  good  definition  should  always  conform  to  two  tests  : 
it  must  be  useful  for  scientific  analysis;  and  it  must 
harmonize  with  popular  and  instinctive  usage.  We  shall 
see  that  the  usual  definitions  of  income  fail  in  one  or  both 
of  these  requisites.  Many  fail  to  lend  themselves  to  scien- 
tific analysis  by  committing  the  fallacy  of  double  counting, 
others  by  confusing  income  and  capital,  while  almost  all  fail 
to  harmonize  with  popular  usage  by  making  out  income 
larger  or  smaller  than  common  sense  would  dictate. 

Like  most  familiar  notions,  the  notion  of  income  seems 
to  the  uninitiated  clear  enough  without  definition.  But 
pitfalls  which  are  unseen  are  for  that  very  reason  all  the 
more  dangerous.  We  shall  point  out  a  few  of  them  by 
criticising,  not  the  specific  definitions  of  particular  authors, 
but  the  general  concepts  of  income  which  the  reader  is 
likely,  more  or  less  unconsciously,  to  have  acquired. 


The  concept  of  income  which  is  the  most  common  is 
that  of  "money-income."  A  business  man's  "money- 
income"  means  to  him  the  money  receipts  from  his  busi- 
ness, less  the  money  expenses  of  obtaining  them.  As 
applied  to  commercial  affairs,  this  concept  is  nearly 
adequate,  and  in  fact  it  coincides,  as  a  special  case,  with  the 
concept  of  income  which  we  have  adopted  ;  for  the 
services  which  a  man's  business  capital  yields  him  usually 
consist  exclusively  of  bringing  him  money,  and  the  disserv- 
ices which  it  causes  him,  of  taking  money  from  him.  Thus 
the  net  value  of  its  services  to  him,  or  difference  between 
the  value  of  the  services  and  disservices,  is  simply  the 
difference  between  the  money  brought  in  and  the  money 
taken  away  from  him  by  his  business. 

But  while  the  concept  of  "money-income"  is  correct  so 
far  as  it  goes,  it  is  far  from  exhausting  the  complete  in- 
come concept.  As  soon  as  we  pass  outside  of  commercial 
circles,  we  find  cases  in  which  money-receipts  are  evi- 


NATURE    OF    CAPITAL   AND   INCOME         [CHAP.  VII 

dently  only  a  part  of  all  receipts  and  money-costs  only 
a  part  of  all  costs.  In  primitive  communities,  and  even  in 
highly  organized  communities,  the  income  of  many  persons 
consists  partly  in  the  acquisition  of  goods  other  than 
money.  The  clergyman  receives,  besides  his  salary,  the 
use  of  a  parsonage ;  and  domestic  servants  receive,  besides 
their  wages,  their  food  and  lodging.  Again,  many  goods 
considered  as  constituting  income  are  not  acquired  by 
exchange  at  all,  but  produced  by  the  individual  himself. 
It  is  usually  recognized  that  a  farmer's  income  includes 
not  only  what  he  gets  in  money  by  sale  and  barter,  but 
what  he  obtains  "in  kind,"  -the  products  of  his  farm 
consumed  by  his  own  family. 

On  the  other  side  of  the  ledger  there  are  many  costs 
which  are  not  in  money  form,  namely,  sacrifices  of  com- 
modities and  labor  in  the  process  of  acquisition.  The 
farmer's  crops  cost  him  labor  as  well  as  wages.  Again, 
he  may  not  pay  money  for  his  seed  and  fertilizer,  but 
sacrifice  for  these  some  of  the  products  of  his  farm 
instead. 

While  the  acknowledged  existence  of  non-monetary  re- 
ceipts and  costs  is  of  itself  a  sufficient  proof  of  the  in- 
adequacy of  the  money-income  idea,  there  is  the  further 
objection  that  money-income  itself  exists,  so  far  as  it  has 
any  existence,  merely  for  the  purpose  of  purchasing 
other  goods.  The  laborer's  wages  are  not  his  "real  wages," 
but  the  means  to  them.  He  transforms  his  money- wages 
into  food,  clothing,  housing,  and  other  uses.  These,  and 
not  the  money  which  buys  them,  constitute  his  real  income. 
If  we  acknowledge  this,  we  are  led  away  from  money- 
income  to  another  concept  common  in  economic  litera- 
ture, but  still  inadequate,  namely,  "real  income." 

§3 

""Real  income"  has  been  denned  in  various  ways,  and, 
like  income  in  general,  is  often  not  defined  at  all.  So 


SEC.  3]  INCOME  10.5 

far  as  it  has  any  recognized  meaning,  it  may  perhaps  be 
expressed  in  the  phrase  "enjoyable  commodities  and  serv- 
ices." This  concept  is  certainly  more  adequate  than 
that  of  money-income;  for  it  includes  the  supplementary 
elements  which  we  found  lacking  under  the  head  of  money- 
income,  such  as  the  clergyman's  use  of  a  parsonage,  the 
servant's  board  and  lodging,  and  the  farmer's  produce  for 
his  own  consumption.  It  is  also  less  superficial  than  the 
concept  of  money-income;  for  it  recognizes  that  money 
is  only  an  intermediary,  and  seeks  to  discover  the  real  ele- 
ments for  which  that  money-income  stands. 

But  the  definition  errs  in  two  particulars :  first,  instead  of 
making  income  consist  simply  and  consistently  of  one  kind 
of  element,  services,  it  attempts  to  include  with  this 
element  the  totally  incongruous  element,  commodities; 
and,  secondly,  it  unnecessarily  restricts  itself  to  enjoyable 
elements;  for,  though  enjoyable  elements  are,  in  the  last 
analysis,  the  final  income  of  society  or  of  an  individual, 
the  fact  that  they  are  should  constitute  the  end  of  our  rea- 
sonings and  not  the  beginning.  We  shall  now  take  up  these 
two  errors  in  order. 

That  the  two  elements  —  " commodities"  and  "services" 
—  form  a  heterogeneous  combination  is  evident  from  the 
fact  that  one  is  concrete  wealth  and  the  other,  abstract  use 
of  that  wealth.  To  bring  about  homogeneity  we  could 
exclude  uses  altogether  and  confine  "income"  to  concrete 
commodities;  or  we  could  exclude  commodities  altogether 
and  restrict  the  term  wholly  to  uses.  The  latter  alter- 
native, which  is  the  solution  offered  in  the  present  book, 
seems  never  to  have  occurred  to  those  who  have  written 
on  the  subject.  The  former  alternative  is  quite  untenable 
and  has  been  instinctively  discarded.  Instead  of  either 
alternative,  the  course  which  has  actually  been  pursued  has 
been  the  eclectic  makeshift  of  including  some  commodities 
and  the  services  or  uses  of  others,  and  even  sometimes  both 
the  commodities  and  the  uses  of  these  very  commodities. 


106  NATURE    OF   CAPITAL   AND   INCOME         [CHAP.  VII 

The  choice  of  the  commodities  to  be  included  has  usually 
fallen  on  the  less  durable  varieties,  such  as  food,  fuel, 
and  clothing,  while  the  objects  the  uses  of  which  have  been 
included  have  been  the  more  durable  instruments, 
such  as  dwelling-houses.  In  the  case  of  intermediate  types, 
such  as  carriages,  furniture,  and  musical  instruments,  no 
fixed  rule  seems  to  have  been  observed.  Some  economists 
are  inclined  to  regard  a  newly  acquired  piano  as  a  part  of 
real  income,  others  to  regard  the  music  which  comes  from 
it  as  the  real  income,  while  still  others  apparently  regard 
both  the  piano  and  its  music  as  real  income.  Evidently 
such  a  patchwork  of  arbitrarily  selected  elements  is  in- 
capable of  furnishing  any  consistent,  reliable,  and  logical 
theory  of  income. 

§4 

The  only  true  method,  in  our  view,  is  to  regard  uniformly 
as  income  the  service  of  a  dwelling  to  its  owner  (shelter 
or  money  rental),  the  service  of  a  piano  (music),  and 
the  service  of  food  (nourishment) ;  and  in  the  same  uni- 
form manner  to  exclude  alike  from  the  category  of  income 
the  dwelling,  the  piano,  and  even  the  food.  These  are  capi- 
tal, not  income;  and  the  instant  we  include  any  such  con- 
crete wealth  under  the  head  of  income,  that  instant  we  begin 
to  confuse  capital  and  income.  The  newly  purchased  or 
newly  constructed  house  is  not  an  element  of  income,  but 
of  capital.  The  income  appears  afterward  in  the  services 
the  house  yields  its  owner,  —  the  shelter  it  affords  through 
subsequent  years  or  the  bringing  in  of  a  money  rent  to  its 
owner.  In  like  manner  the  newly  acquired  piano  and  loaf 
of  bread  are  not  income,  but  capital.  Their  income  fol- 
lows later  in  the  form  of  piano  music  and  nourishment. 

No  reason  has  ever  been  given  why  the  short-lived  bread 
should  be  treated  differently  from  the  long-lived  dwelling. 
The  use  of  the  bread  is  just  as  distinct  from  the  bread  as 
the  use  of  the  dwelling  is  distinct  from  the  dwelling.  The 


SEC.  4]  INCOME  107 

difference  between  the  case  of  the  bread  and  that  of  the 
dwelling  is  purely  one  of  degree.  The  uses  of  the  bread  fol- 
low the  acquisition  of  the  bread  almost  instantly,  whereas 
the  uses  of  the  dwelling  are  not  completely  ended  until 
many  years  after  the  dwelling  is  acquired.  From  this 
difference  in  time  comes  a  corresponding  difference  in  value. 
The  value  of  the  use  of  the  bread  is  practically  identical 
with  the  value  of  the  bread.  A  man  will  give  ten  cents  to- 
day for  a  loaf  if  he  expects  its  use  (consumption)  to-morrow 
to  be  worth  ten  cents.  The  value  of  the  dwelling,  however, 
will  be  less  than  the  value  of  its  prospective  uses,  owing  to 
the  fact  that  these  uses  are  so  remote  in  the  future.  If 
the  dwelling  is  expected  to  last  fifty  years,  and  its  shelter 
to  be  worth  $1000  a  year,  this  $50,000  worth  of  shelter  will 
not  by  any  means  be  worth  $50,000  in  advance,  but  only, 
say,  $15,000.  This  "capitalized"  value  of  the  expected 
uses  of  the  dwelling  will  be  the  value  of  the  dwelling.  In 
short,  the  bread  and  its  uses  are  practically  contemporane- 
ous and  equal  in  value,  whereas  the  dwelling  and  its  uses 
are  widely  diverse  in  both  particulars.  Consequently  it 
has  not  seemed  worth  while  to  economists  to  distinguish 
between  the  bread  and  its  uses;  whereas  they  could  not 
help  distinguishing  between  the  dwelling  and  its  uses. 

But  in  science,  logical  distinctions  are  inexorable, 
and  their  violation  always  brings  retribution.  It  may 
be  said  in  truth  that  if  economists  had  been  scrupu- 
lous enough  to  distinguish  a  loaf  of  bread  from  its  uses, 
they  would  have  escaped  most  of  the  confusions  which 
have  so  long  enveloped  the  theory  of  income.  Having 
once  chosen  as  the  income  element  the  food  instead  of  its 
use,  economists  have  proceeded  to  do  the  same  in  the  case 
of  clothing  and  other  moderately  durable  commodities. 
Naturally  they  have  not  known  where  to  cease  calling  the 
concrete  instrument  income  and  begin  calling  its  use  income 
instead.  In  their  hesitation  they  have  in  some  cases  ended 
by  including  both.  By  so  doing  they  commit  the  fallacy 


108  NATURE    OF    CAPITAL   AND   INCOME         [CHAP.  VII 

of  double  counting.  This  fallacy  they  escape  only  in  the 
case  of  the  very  durable  instruments,  such  as  the  dwelling, 
and  the  very  perishable  instruments,  such  as  the  bread. 
The  dwelling  is  too  evidently  not  income  ever  to  be  so 
regarded,  and,  as  to  bread,  one  of  the  two  elements — its 
use — is  overlooked  altogether.  But  it  is  felt  that  inter- 
mediate types,  like  the  piano,  are  as  fairly  entitled  to  be 
called  income,  when  acquired,  as  the  bread,  and  that  their 
services  are  as  fairly  entitled  to  be  called  income  as  are  the 
services  of  the  dwelling.  Consequently  both  are  deemed 
income.  But  a  piano  valued  at  $500  is  so  valued  because 
this  sum  is  the  capitalized  value  of  the  future  expected 
uses  which,  let  us  say,  are  $600,  distributed  over  the 
lifetime  of  the  instrument.  Consequently  if,  when  the 
piano  is  first  purchased,  it  is  entered  as  real  income  to 
the  extent  of  $500,  and  then  later  its  subsequent  services 
in  providing  its  owner  with  music  are  also  counted  as 
income  to  the  extent  of  $600,  it  is  clear  that  there  has 
been  double  (though  successive)  counting.  The  services 
of  the  piano  have  been  counted  as  income  in  anticipation 
as  well  as  in  realization. 

Yet  this  error,  in  one  form  or  another,  is  not  infrequently 
committed.  It  is  virtually  in  this  way  that  Cannan *  and 
others  regard  "savings"  as  income  in  the  year  in  which 
the  savings  are  accumulated,  although  the  interest  upon 
those  savings  will  be  counted  as  income  in  subsequent 
years.  The  nature  of  the  fallacy  is  seen  as  soon  as 
we  translate  from  money  to  other  instruments.  If  a 
man  saves  up  money  and  purchases  an  automobile, 
it  is  clearly  double  counting  to  call  the  automobile  thus  ob- 
tained "real  income,"  and  then  include  its  subsequent  uses 
in  the  real  income  of  ensuing  years.  It  does  not  matter 

1  Elementary  Political  Economy,  London,  1888,  pp.  58,  59.  The 
fallacy  of  including  savings  in  income  will  be  treated  at  greater 
length  in  Chap.  XIV.  The  reader  who  believes  that  savings  ought  to 
be  regarded  as  income  is  asked  to  stay  judgment  until  he  has  finished 
Chap.  XIV. 


SEC.  5]  INCOME  109 

how  durable  the  instrument;  it  is  always  double  counting 
to  include  the  instrument  and  its  uses.  The  savings  may 
be  invested  in  land  or  in  confectionery.  The  only  true 
income  is  the  use  of  the  land  or  the  use  of  the  confec- 
tionery. To  include  also  the  value  of  the  land  or  the 
value  of  the  confectionery  is  to  count  as  income  the  capi- 
talization of  income. 


Economists  have  been  more  or  less  aware  of  the  pitfall 
of  double  counting,  but  not  of  the  reason  for  it.  They 
have  therefore  attempted  to  avoid  it,  not  by  excluding  all 
commodities  from  the  income  concept  and  restricting  it  to 
services,  but  by  specifically  excluding  from  income  certain 
groups  of  commodities.  Naturally,  they  have  been  at 
a  loss  to  formulate  a  satisfactory  and  logical  principle  for 
this  exclusion.  Some  of  them  have  no  better  suggestion  to 
offer  than  that  all  " large"  or  " unusual"  acquisitions  should 
be  ruled  out,  and  that  only  those  commodities  which  come 
into  a  man's  possession  in  a  "regular"  stream  shall  be  en- 
titled to  the  name  income.  This  makeshift  has  received 
much  currency  among  German  writers.  To  be  sure,  it 
serves  the  purpose  of  excluding  from  income  such  obvi- 
ously inappropriate  elements  as  bequests  and  gifts  of  large 
fortunes.  It  is  clear  that  when  a  well-known  millionaire 
recently  fell  heir  to  seventy  millions,  this  did  not  con- 
stitute his  income  for  the  year  in  which  he  received  it,  but 
that  it  merely  constituted  the  principal  or  capital  from 
which  he  would  receive  income  in  subsequent  years.  But 
the  reason  that  it  is  improper  to  call  this  suddenly  acquired 
fortune  income  is  not  that  it  was  large,  nor  that  it  was 
sudden,  but  that  it  consisted  of  rights  to  concrete  wealth 
—  factories,  ships,  railways,  and  dwellings.  These  things 
are  not  under  any  circumstances  income,  but  yield  income 
through  future  uses.  It  is  idle  to  call  income  "regular"; 
for  we  all  know  that  it  is  irregular. 


110  NATURE    OF   CAPITAL    AND    INCOME         [CHAP.  VII 

Another  but  very  similar  attempt  to  escape  the  difficulties 
of  double  counting  and  of  confusing  capital  and  income  is 
to  specify,  not  that  income  must  in  a  vague  way  be  "regu- 
lar/' but  that  it  must  be  such  as  to  leave  unimpaired  the 
capital  which  yields  it.1  Such  a  definition  has  the  merit 
of  connecting  income  with  capital  as  its  source,  but  it  merely 
shifts  the  pretended  attribute  of  uniformity  from  the 
income  itself  to  its  parent  capital.  In  actual  fact  it 
is  seldom  true  either  that  income  flows  uniformly  or  that 
capital  remains  at  a  constant  level.  To  stipulate  such  uni- 
formity as  a  necessary  limitation  of  income  is  to  define,  not 
the  actual  irregular  income  which  exists  in  fact,  but  an 
ideal  standard  which  we  set  up  for  reference.  It  cannot 
be  denied  that  the  term  "income"  is  sometimes  used  in  the 
sense  of  such  an  ideal  instead  of  in  the  sense  of  actual  in- 
come ;  and  we  shall  follow  this  usage  so  far  as  to  call  such 
an  ideal  by  the  name  of  "standard  income."  What  we 
insist  on  is  that  such  standard  income  is  not,  and  must  not 
be  confused  with,  the  actual  income  which  a  man  receives 
from  his  capital.  It  is  simply  the  income  which  he  would 
receive  if  he  chose  to  keep  his  capital  unimpaired  and  un- 
increased.  If  a  man  has  his  capital  invested  in  the  form  of 
a  house  which  yields  him  rent,  this  actual  rent,  less  any 
actual  expenses  for  repairs,  taxes,  etc.,  is  his  income 
from  that  house,  even  though  the  house  may  be  depreciat- 
ing in  value.  The  ideal  or  standard  income  whi  h  the  house 
might  yield  without  depreciation  will  be  somewhat  lower 
than  this  actual  income,  the  difference  being  what  is  called 
amortization. 

This  is  not  the  place  to  discuss  amortization  and  the  rela- 
tions subsisting  between  standard  and  real  income.  These 
topics  will  be  fully  discussed  in  Chapter  XIV.  We  are  at 
present  concerned  with  actual,  not  ideal,  income;  so 

1  This  specification  is  characteristic  of  Hermann,  Schmoller,  and 
many  others.  See  Kleinwachter,  Das  Eifikommen  und  seine  Vertcilitng, 
pp.  22-23. 


SEC.  5]  INCOME  111 

far  as  popular  usage  goes,  it  gives  its  sanction  to  the  use  of 
the  term  "  income  "  in  the  one  sense  quite  as  much  as  in  the 
other,  though  usually  with  very  little  intelligent  discrimi- 
nation between  the  two.  For  instance,  a  life  annuity  from 
an  insurance  company,  or  a  pension  from  a  government, 
is  universally  recognized  as  "income."  Yet  this  income 
trenches  on  the  capital  which  produces  it,  eating  it  up  year 
by  year  until,  at  the  end  of  its  allotted  period,  it  is  entirely 
exhausted.  Let  us  suppose  that  the  annuity  is  one  of  $1000 
a  year  for  twenty  years.  Reckoning  interest  at  five  per  cent, 
such  an  annuity  is  worth,  by  the  actuaries'  tables,  $12,462. 
That  is,  the  annuitant  could  sell  his  annuity,  on  a  five 
per  cent  basis,  for  $12,462  in  ready  money.  But  this 
$12,462  invested  at  five  per  cent  would  bring  in,  with- 
out impairing  the  principal,  not  $1000  a  year,  but 
only  $623.10.  If  then  he  actually  gets  $1000  he  is 
trenching  on  his  capital  the  first  year  to  the  extent  of 
$376.90.  Yet  we  regard  him,  and  very  properly  too,  as 
having  a  true  income  of  $1000  a  year. 

If  it  were  true  that  income  could  never  trench  on  capital, 
we  could  not  reckon  a  laboring  man's  wages  as  income 
without  first  deducting  a  premium  or  sinking  fund  sufficient 
to  provide  for  the  continuance  of  this  income  after  the  de- 
struction by  death  of  the  laborer.  If  the  annuitant  or 
laborer  should  actually  set  aside  such  an  annual  sum  as  to 
maintain  the  capital  value  of  his  property  unimpaired,  we 
should  be  quite  justified  in  considering  the  net  sum,  and 
not  the  gross  sum,  as  income.  The  $1000  annuitant  who 
pays  $376.90  annually  into  a  sinking  fund  is  getting 
only  $623.10  annually,  not  $1000,  for  an  income,  and  the 
laboring  man  who  pays  an  insurance  premium  reduces  his 
income  by  that  amount.  It  surely  makes  a  difference 
whether  these  "sinking  funds"  or  "premiums"  are  actually 
set  aside  or  merely  reckoned.  To  reckon  what  one  ought 
to  save  in  order  to  maintain  capital  is  not  to  save  it, 
and  a  definition  of  income  which  depends  upon  an  ideal 


112  NATURE   OF   CAPITAL  AND   INCOME        [CHAP.  VII 

reckoning    instead    of  a  real  payment  is   to  that  extent 
inadequate. 

We  have  now  seen  how  the  fatal  inclusion  of  concrete 
wealth  by  the  side  of  abstract  services  as  a  part  of  income 
has  led  economists  into  two  errors,  —  one  the  confusion  of 
capital  with  income,  and  the  other  the  fallacy  of  double 
counting.  We  now  proceed  to  consider  the  other  mistake 
in  the  ordinary  concept  of  real  income,  namely,  that  due 
to  the  needless  restriction  introduced  by  the  term  "enjoy- 
able." Real  income,  we  were  told,  consists  of  "enjoyable 
commodities  and  services."  We  have  thus  far  succeeded 
in  eliminating  "commodities"  from  this  formula;  we  now 
proceed  to  show  that  we  may  also  eliminate  "enjoyable," 
and  leave  the  very  simple  formula:  Income  consists  of 
services. 

It  is  quite  true  that  when  we  put  together  all  the 
elements  which  go  to  make  up  the  total  income  of  a  com- 
munity or  of  an  individual,  and  deduct  all  the  negative 
elements,  or  outgoes,  we  shall  find  that  there  are  then  left 
solely  enjoyable  services.  But  the  various  elements  which 
are  thus  combined  —  the  income  from  factories,  mines, 
farms,  and  other  instruments  or  groups  of  instruments  — 
do  not  all  consist  of  enjoyable  services.  Most  of  them 
consist  of  intermediate  services  preparatory  to  enjoyable 
services.  How  these  intermediate  services  cancel  them- 
selves out  in  the  final  summation  will  form  the  subject 
of  a  future  chapter.  At  present  we  are  merely  concerned 
in  pointing  out  that  any  adequate  concept  of  income  must 
leave  room  for  these  intermediate  services,  i.e.  for  the 
income  rendered  by  a  factory  or  a  bank  as  well  as  that 
yielded  by  a  dwelling  or  a  pleasure  yacht.  We  have  already 
had  occasion  to  note  the  inadequacy  of  that  concept  of 
income  which  restricts  it  to  the  yielding  of  money;  we  now 
need  to  observe  the  inadequacy  of  that  concept  which 


SEC.  7]  INCOME  113 

goes  to  the  opposite  extreme  and  leaves  money  income 
out  of  account  altogether.  Having  found  "money  income " 
insufficient  for  their  purposes,  economists  have  conceived 
of  "real  income."  But  by  making  real  income  consist  of 
"enjoyable"  elements,  they  have  excluded  money  income 
altogether.  Some  of  them  more  or  less  avowedly  retain 
both  concepts,  but  they  do  not  show  how  to  coordinate  them 
nor  how  to  include  them  both  under  a  more  general  income- 
concept.  In  their  minds  the  two  seem  to  stand  totally  dis- 
connected, except  that,  in  a  partial  and  incomplete  way, 
real  income  is  thought  of  as  that  for  which  money  income 
is  spent. 

§7 

The  ordinary  concepts  of  income  fail  to  conform  to  any 
consistent  scheme  whatever.  In  consequence,  among  other 
needless  distinctions,  are  those  which  have  been  drawn 
between  social  and  individual  income. 

Social  income  has  usually  been  conceived  as  the  "net 
product "  of  society,  —  not  in  the  sense  of  the  net  difference 
between  services  and  disservices,  but  in  a  sense  which 
includes  commodities.  No  consistent  method  of  reckoning 
this  net  product  has  been  furnished.  It  is  clear  that  we 
cannot  include  all  products.  Some  are  only  too  evidently 
newr  capital,  such  as  newly  constructed  railways,  steam- 
ships, tunnels,  bridges,  and  buildings  and  would  not  be 
included  by  most  persons  in  social  income.  Others  must 
certainly  be  omitted  to  avoid  duplication  in  our  reckoning. 
If  we  were  to  include  the  wheat  crop  of  the  fanner,  the 
flour  of  the  miller,  and  the  bread  of  the  baker,  we  would 
be  counting  the  same  thing  three  times  over,  —  once  for 
each  of  three  successive  processes.  Some  economists  have 
sought  to  avoid  this  repetition,  either  by  excluding  the  pro- 
duction and  consumption  of  raw  materials,  or,  if  these  are 
included,  by  not  including  the  whole  value  of  the  finished 
product,  but  only  the  increment  of  value  over  that  of  the 
raw  materials. 


114  NATURE   OF   CAPITAL   AXD   INCOME        [CHAP.  VII 

"We  must  be  careful  not  to  count  the  same  thing  twice.  If  we 
have  counted  a  carpet  at  its  full  value,  we  have  already  counted  the 
values  of  the  yarn  and  the  labour  that  were  used  in  making  it;  and 
these  must  not  be  counted  again.  But  if  the  carpet  is  cleaned  by 
domestic  servants  or  at  steam  scouring  works,  the  value  of  the  labour 
spent  in  cleaning  it  must  be  counted  separately;  for  otherwise  the 
results  of  this  labour  would  be  altogether  omitted  from  the  inventory 
of  those  newly-produced  commodities  and  conveniences  which  consti- 
tute the  real  income  of  the  country."  1 

These  reservations  are  entirely  correct;  but  they  fur- 
nish no  general  means  of  avoiding  double  counting.  For 
instance,  are  fuel  and  labor  to  be  deducted  in  the  same 
way  as  raw  materials  ?  Some  writers  have  gone  so  far  as 
to  claim  that,  just  as  the  cost  of  feeding  work  animals 
must  be  deducted  from  the  value  of  the  work  they  do,  so 
the  cost  of  supporting  laborers  must  be  deducted  from  the 
value  of  their  product.2  If  this  view  were  correct,  it  would 
seem  that  the  laborer  could  not  share  at  all  in  the  distri- 
bution of  the  social  income,  since  all  that  comes  to  him 
is  deducted ! 

A  similar  question  as  to  deductions  arises  in  the  oft- 
cited  case  where  one  profession  is  more  disagreeable  or 
irksome  than  another.  Should  any  deduction  be  made 
from  the  income  of  the  hangman,  for  instance,  to  equalize 
his  net  income  with  the  net  income  of  a  more  desirable 
calling  ? 

When  social  income  is  called  "net  product,"  the  same 
question  arises  which  was  met  with  in  the  case  of  individual 
income,  viz.,  whether  by  "product"  is  meant  concrete 
wealth,  or  services,  or  both.  In  our  own  theory,  "services" 
are  taken,  but  the  usual  concepts  adopt  wealth,  or  both 
wealth  and  services.  According  to  them,  part  of  the  in- 
come of  society  consists  of  new  wealth,  such  as  factories, 
sihps,  and  dwellings,  while  the  services  of  these  new  creations 

1  Marshall,  Principles  of  Economics,  Vol.  I,  p.  150. 

2  E.g.    "  Report  of  Committee  on  a  Common  Measure  of  Value  in 
Direct  Taxation,"   Report  of  British  Association  for  Advancement  of 
Science,  1878,  p.  220. 


SEC.  7]  INCOME  115 

figure  as  income  in  future  years.  We  have  already  observed 
that  to  count  a  new  dwelling  or  piano  as  income  this  year, 
and  its  use  as  income  in  succeeding  years,  is  a  species  of 
double  counting  as  well  as  a  confusion  of  capital  and  income. 
Both  of  these  errors  are  repeated  in  any  concept  of  social 
income  which  includes  at  once  additions  to  the  world's 
wealth,  and  the  income  which  this  very  wealth  subse- 
quently yields. 

§8 

When  a  wrong  road  is  once  taken,  it  almost  inevitably 
happens  that  it  leads  those  who  follow  it  further  and  fur- 
ther astray.  Economists,  having  selected  a  wrong  idea 
of  income  to  start  with,  naturally  found  it  so  ill  suited  to 
their  purposes  that,  in  each  problem  to  which  they  at- 
tempted to  apply  it,  some  special  interpretation  or  amend- 
ment became  necessary,  until,  instead  of  one  concept, 
they  became  possessed  of  a  miscellaneous  assortment1  of 
concepts !  They  have  been  compelled  not  only  to  dis- 
sociate money-income  and  real-income,  but  also  to  disso- 
ciate the  income  of  the  individual  and  the  income  of  society. 
When  it  is  understood  that  the  entire  and  only  contribution 
to  the  income  stream  which  any  given  instrument  of  capital 
can  make  consists  in  the  services  which  that  instrument 
renders,  it  will  be  found  that  all  subsidiary  meanings  of 
income  are  simply  incomes  from  particular  instruments 
or  groups  of  instruments.  If  the  instrument  in  question  is  a 
private  carriage,  the  services  which  it  brings  forth,  as  events 
desirable  to  its  owner,  are  the  acts  of  conveying  him  from 
one  place  to  another.  These  are  primary  or  natural-income. 
If  the  instrument  is  a  public  carriage,  the  services  which  it 
brings  forth,  as  events  desirable  to  its  owner,  are  the  pay- 
ments of  fares.  These  are  money-income.2  If  the  group  of 

1  The  reader  who  cares  to  study  them  in  detail  will  find  a  collec- 
tion of  definitions  in  the  Appendix  to  Chapter  VII. 

2  It  should  be  borne  in  mind  that  the  income  is  not  the  money 
itself,  which  is  a  concrete    commodity,  but   the  bringing  in   of   the 
money,  which  is  an  abstract  service. 


116  NATURE   OF   CAPITAL   AND    INCOME        [CHAP.  VII 

instruments  is  the  entire  group  of  instruments  constituting 
the  entire  capital  of  a  community,  the  net  total  of  their 
services  and  disservices  is  the  entire  income  of  the  com- 
munity. This  is  social  income.  If  the  group  be  the  entire 
property  of  an  individual  —  the  rights  which  he  owns, 
complete  or  partial,  in  instruments  —  the  net  total  of  the 
services  and  disservices  to  which  he  is  thus  entitled  consti- 
tutes his  income.  This  is  individual  income. 

In  science,  the  chief  test  of  a  definition  is  its  adaptability 
to  analysis.  Judged  by  this  test,  none  of  the  current  con- 
cepts of  income  which  we  have  passed  in  review  can 
claim  to  be  adequate;  for  we  have  found  them  subject  to 
the  confusions  of  capital  and  income,  and  of  double  count- 
ing. A  secondary  test  is  that  a  working  definition  should 
also  fit  into,  or  rather,  give  clear  and  consistent  outlines 
to  the  vague  notions  of  income  which  we  find  ready  made  in 
the  actual  world  of  business  and  accounts. 

Of  our  own  concept  of  income,  as  consisting  exclusively 
of  services,  we  shall  endeavor  to  show  that  it  includes  the 
commercial  bookkeeper's  concept  of  "money  income"; 
that  it  is  coextensive  with  the  popular  notions  of  income, 
including  what  those  notions  include  and  excluding  what 
they  exclude ;  that  it  affords  a  place  for  the  usage  by  which 
.sinking  funds  are  reckoned  and  justifies  the  phrase  "living 
beyond  income";  that  it  avoids  double  counting  auto- 
matically and  without  the  necessity  for  the  exercise  of  judg- 
ment in  each  special  case;  that  it  makes  capital  and  income 
strictly  correlative  but  never  in  danger  of  being  confused; 
and  last,  but  not  least,  that  it  lends  itself  readily  to  economic 
analysis  and  serves  as  a  foundation  for  the  theory  of  interest. 

The  concept  of  income  to  be  elaborated  is  similar  to 
several  which  have  been  put  forward  by  other  writers. 
It  is  almost  identical  with  that  of  Edwin  Caiman;1  it 

1  Sr-o  Ififtorjf  of  the  Theory  of  Production  and  Distribution;  Elemen- 
tary Political  Economy;  and  "What  is  Capital?"  Economic  Journal, 
1897. 


Sec.  8J  INCOME  117 

also  harmonizes  with  what  Professor  Marshall  l  calls 
the  "usance"  of  wealth,  and  with  the  psychological 
concepts  of  income  in  President  Hadley's  Economics?  in 
Professor  Flux's  Economic  Principle*,3  and  in  Professor 
Fetter's  Principles  of  Economics. 4  Finally,  it  harmonizes 
more  closely  than  at  first  glance  might  be  supposed,  with 
the  etymological  and  popular  meaning  of  income.  In- 
come from  any  source  is  what  comes  in  from  that  source. 
The  income  from  any  capital  is  what  that  capital  brings  in 
to  its  owner,  no  matter  what  may  be  the  form  of  benefit 
brought  in.  If  the  capital  serves  to  bring  in  money,  the 
income  is  "money-income."  If  it  serves  to  bring  in  crops 
or  products,  as  does  a  self-supporting  farm,  the  income  is 
of  another  form.  If  it  serves  to  bring  in  enjoyable  com- 
forts, as  does  a  dwelling  house,  the  income  is  of  a  still 
different  form.  But  in  all  cases,  the  essential  fact  is  that 
the  capital  performs  service,  —  accomplishes  something 
desired. 

As  this  usage  makes  income  include  all  money-income,  it 
cannot  be  maintained  that  it  conflicts  with  commercial 
usage.  It  may  be  objected  by  the  unreflecting  that  by 
including  non-monetary  elements  it  includes  too  much; 
but  many  —  often  all  —  of  the  non-monetary  benefits  con- 
ferred by  capital  are  recognized  as  income  by  economists, 
as  well  as  by  such  men  of  affairs  as  have  studied  the 
subject  with  care.  A  business  man  who  had  bought  a 
yacht  remarked:  "It's  a  good  investment,  and  I  get  my 
dividends  every  Saturday  afternoon  when  I  take  a  sail  in 
it."  And  the  writer  has  never  had  any  difficulty  in  per- 
suading other  business  men  of  the  propriety  of  such  usage. 
In  fact,  without  an  enjoyable  use  in  prospect,  money-income 
itself  would  have  no  existence  or  meaning.  A  house  could 

1  See  Principles  of  Economics.  3d  ed.  (Maemillan).  Vol.  I,  p.  156. 
A  part  of  this  passage  is  quoted  in  Appendix  to  Chap.  VII.  See  also 
Carver's  Distribution  of  Wealth  (New  York.  Marmilkm,  1904),  p.  123. 

•  Chap.  I.  3  p.  17.  4  p;).  43,  571. 


118  NATURE    OF   CAPITAL   AND   INCOME         [CHAP.  VII 

never  command  a  money  rent  to  the  landlord  if  it  did 
not  also  yield  shelter  to  the  tenant,  and  even  from  the 
standpoint  of  the  landlord  the  receipt  of  the  money  only 
intervenes  as  a  medium  for  payment  of  his  own  rent  and 
other  expenses  of  living,  in  other  words  for  securing  his 
enjoyable  income. 

Income  is,  then,  a  very  general  concept.  It  consists  of 
services  rendered  by  capital.  We  have  seen  that  under  it 
are  included  several  special  concepts :  Social  income,  indi- 
vidual income,  money  income,  natural  income,  and  enjoyable 
income.  We  shall  soon  see  that  the  net  income  of  society 
or  of  an  individual  consists  wholly  of  enjoyable  income. 
This  is  because  the  non-enjoyable  elements  of  income, 
such,  for  example,  as  money-income,  are  all  exactly  offset 
by  equal  items  of  outgo.  But  the  non-enjoyable  elements 
are  none  the  less  a  part  in  the  grand  total,  and,  in  fact, 
by  far  the  greater  part.  The  money-income  of  ordinary 
bookkeeping  forms  the  bulk  of  any  true  inventory  of  in- 
come; but  its  significance  cannot  be  understood  until  its 
counterpart  in  outgo  is  also  taken  into  account,  nor  until, 
in  fact,  a  complete  picture  of  all  elements  of  income  is 
brought  before  the  mind's  eye.  To  present  this  picture 
will  be  the  object  of  the  next  three  chapters. 


CHAPTER   VIII 

INCOME   ACCOUNTS 
§1 

THE  income  of  our  capital,  then,  is  simply  that  which 
it  does  for  us.  Whether  it  brings  us  money  or  other  return 
does  not  matter;  the  flow  of  its  services  is  its  income. 
These  services  of  wealth,  as  was  previously  explained,  con- 
sist of  any  desirable  events  which  occur  by  means  of  that 
wealth  or  any  undesirable  events  prevented. 

Services  exist  in  infinite  variety.  All  work  done  by 
human  beings,  all  the  operations  of  industry,  all  the  trans- 
actions of  commerce,  are  services,  and  enter  into  income 
accounts.  A  bird's-eye  view  of  this  busy  planet  would  reveal 
wealth  —  real  estate,  commodities,  and  human  beings,  — 
ceaselessly  at  work  performing  services.  Land,  men,  and 
implements  are  changing  land,  seed,  and  live  stock  into 
grain,  beef,  lumber,  and  steel.  Manufacturing  plants  are 
converting  raw  materials  into  flour,  furniture,  cloth,  and 
implements.  In  domestic  establishments  we  find  the  serv- 
ices of  cooking,  warming,  cleaning,  and  sheltering.  Agri- 
culture, mining,  transportation,  and  commerce  are  simply 
names  that  we  give  to  the  group  of  services  performed  by 
farm,  mine,  railroad,  and  business  capital. 

A  disservice  is  a  negative  service.  It  is  an  undesirable 
event  occasioned,  or  a  desirable  one  prevented,  by  means  of 
an  article  of  wealth.  A  flow  of  disservices  or  negative  in- 
come is  called  outgo.  It  does  not  matter  whether  the  outgo 
occasioned  by  an  article  consists  in  depriving  the  owner 
of  money  or  in  some  other  evil.  If  the  outgo  is  in  mone- 

119 


120  NATURE    OF   CAPITAL   AND   INCOME       [CHAP.  VIII 

tary  form  it  is  called  expense;  if  it  is  in  the  form  of  human 
exertion  it  is  called  labor.  It  includes  all  of  what  economists 
have  called  cost,  i.e.  labor,  trouble,  expense,  and  sacrifices  of 
all  kinds. 

An  instrument  very  seldom  yields  services  without  in- 
volving some  disservices.  A  dwelling  house,  for  instance, 
not  only  gives  off  services  called  shelter,  but  also  occasions 
disservices  in  the  form  of  labor  (or  expense)  for  renewals, 
painting,  cleaning,  caretaking,  insurance,  and  taxes.  Any 
disagreeable  event  occasioned  by  that  house  is  a  disservice, 
just  as  any  agreeable  event  is  a  service.  Again,  while 
a  saddle  horse  performs  services  in  giving  its  owner  a 
daily  ride,  it  performs  disservices  in  being  stabled,  fed, 
and  shod.  A  farmer  gets  services  out  of  his  land  when  it 
yields  him  crops;  but  to  get  these  services  he  has  to  put 
fertilizer,  seed,  labor,  and  expense  into  that  land.  A  rail- 
way performs  a  vast  service  of  transportation,  hauling 
passengers  and  commodities,  but  it  requires  a  prodigious 
amount  of  coal,  supplies,  and  labor  to  keep  it  going. 

Disservices  are  not  essential  to  the  idea  of  wealth;  an 
article  of  wealth  sometimes  offers  services  without  any  dis- 
services. When  disservices  exist  they  are  usually  over- 
balanced, in  the  estimation  of  the  owner,  by  prospective 
services.  As  soon  as  the  disservices  of  an  article  of  wealth 
preponderate,  in  the  est  mation  of  its  owner,  over  the  serv- 
ices, it  is  regarded  as  "more  trouble  than  it  is  worth," 
is  cast  aside  and  ceases  to  be  wealth.  In  the  meantime 
such  articles,  if  regarded  as  owned  at  all,  constitute  a 
sort  of  wealth  of  negative  utility,  —  Jevons  calls  them 
"discommodities."  They  are  never  of  great  importance 
and  need  receive  no  special  attention.  The  chief  examples 
of  such  articles  are  garbage,  ashes,  sewage,  carrion,  rubbish, 
and  waste. 

It  has  already  been  observed  that  services  and  disserv- 
ices, like  wealth,  are  measured  in  two  ways  —  in  quantity 
and  value  —  and  that  the  quantity  of  each  service  is 


SEC.  2]  INCOME   ACCOUNTS  121 

measured  in  its  own  special  unit.  The  quantity  of  the  serv- 
ices of  a  gardener  is  often  measured  by  the  number  of 
hours  he  works;  the  services  of  a  windmill,  by  the  number 
of  gallons  of  water  pumped.  Quantities  of  services  (or 
disservices)  are  thus,  like  instruments  of  wealth,  very  hetero- 
geneous and  are  incapable  of  being  combined  in  a  single  sum. 
To  obtain  a  homogeneous  mass  of  value,  we  must  multiply 
the  quantity  of  services  (or  disservices)  by  their  several 
prices. 

Income  and  outgo,  then,  like  capital,  are  used  in  two 
senses:  income-services  (as  well  as  outgo-disservices)  and 
income-value  (as  well  as  outgo-value).  Hereafter,  when 
the  terms  "income"  or  "outgo"  are  used  alone,  the  value 
sense  will  be  understood. 

The  value  of  any  individual  service  or  disservice  con- 
stitutes an  element  of  income  or  outgo.  The  value  of  all 
the  services  flowing  from  an  article  of  wealth  through  any 
period,  that  is,  the  sum  of  all  the  elements  of  income,  is 
called  its  gross  income.  The  excess  of  the  gross  income 
over  the  outgo,  in  other  words,  the  algebraic  or  net  sum 
of  all  elements  of  income  and  outgo,  is  the  net  income.  If, 
instead  of  an  excess,  there  is  a  deficiency,  it  is  called  net 
outgo.  Net  income  is  of  far  more  importance,  both  in 
practice  and  in  theory,  than  gross  income.  Gross  income 
may  often  be  measured  in  more  than  one  way,  according 
as  the  elements  of  which  it  is  composed  are  considered 
with  or  without  accompanying  offsets ;  but  the  sum  called 
net  income  will  be  the  same  in  either  case. 

§2 

Income  (or  outgo)  always  implies  (1)  capital  as  the 
source,  and  (2)  an  owner  of  capital  as  the  beneficiary. 
Mr.  Smith's  income  from  his  farm  implies  that  the  farm 
yields  the  income  and  that  Mr.  Smith  receives  it.  In  this 
book  we  shall  need  to  consider  income  chiefly  in  its  rela- 
tion to  the  capital  yielding  it  rather  than  in  its  relation  to 


122  NATURE    OF    CAPITAL   AND    INCOME      [CHAP.  VIII 

the  owner  receiving  it.1  This  twofold  aspect  of  income  is 
expressed  in  accounts  by  regarding  the  farm  as  "in  account 
with  "  its  owner.  All  income  from  it  to  him  is  placed  on  one 
side  of  the  ledger  and  is  said  to  be  "credited"  to  the  farm, 
while  its  outgo  is,  in  like  manner,  "debited."  A  credit 
item,  then,  signifies  income  which  is  yielded  by  a  given 
capital,  and  a  debit  item  signifies  outgo  which  it  occasions. 
The  terms  refer  respectively  to  positive  and  negative  ele- 
ments in  the  income  and  outgo  accounts  of  that  capital. 

We  are  now  in  a  position  to  apply  the  foregoing  defini- 
tions to  income  accounts.  We  begin  by  imagining  a  "house 
and  lot"  as  an  article  of  wealth  or  capital,  and  shall  first 
consider  its  income  and  outgo  during  the  period  of  the  cal- 
endar year  1900.  The  income  which  this  capital  brings 
in  to  its  owner  may  be  either  a  money  rental  or  the  serv- 
ices of  shelter  for  himself  and  family.  In  either  case  the 
income  may  be  measured  in  money,  although  in  the  case  of 
occupancy  by  the  owner  this  measurement  requires  a  special 
appraisement.  We  shall  suppose  that  the  house  was  built 
many  years  ago  and  in  1900  is  nearly  worn  out.  It  yields 
an  income  worth  $1000  a  year.  Against  this  income  there 
are  offsets  in  the  form  of  repairs,  taxes,  etc. ;  for  these  pay- 
ments are  "undesirable  events"  occasioned  by  the  house 
and  lot.  We  have,  then,  the  following  "income  account"  : 

INCOME  FOR  HOUSE  AND  LOT  DURING  YEAR  1900 
Income  Outgo 

Use  of  house  and  lot   .     .     $1000     Repairs $200 

Taxes 100 

Insurance   .  100 


$1000  $400 

The  net  income  is  therefore  $600. 

1  The  terms  income  and  outgo  are  somewhat  unfortunate,  as, 
etymologically,  they  suggest  the  relation  to  the  owner  Smith  rather 
than  to  its  source,  the  farm.  Smith's  income  is  the  farm's  "out- 
come" or  "yield"  (in  German,  ertrag).  Similarly,  when  the  farmer 


SEC.  2]  INCOME   ACCOUNTS  123 

Next  year  we  may  suppose  that  the  house  is  found  to 
have  rotted  beams,  is  condemned,  and  must  be  abandoned 
or  torn  down.  Its  services  are  ended,  but  the  land  is  still 
good  and  the  owner  can  build  a  new  house.  This  operation 
consumes,  let  us  say,  the  first  six  months  of  the  year  1901, 
so  that  during  that  period  there  is  no  income,  but  only  outgo. 
During  the  second  half  of  the  year  the  house  is  occupied  and 
its  use  is  valued  at  $600.  In  the  first  six  months  not  only 
did  the  "house  and  lot"  fail  to  yield  any  income,  but  on  the 
contrary  occasioned  an  expense.  The  cost  of  production  of 
the  house  was  a  disservice;  for  this  was  an  "undesirable 
event"  occasioned  by  the  house  and  lot.  It  was  withstood 
only  for  the  sake  of  future  services  which  it  would  bring  in 
its  wake.  It  was  not  itself  a  desirable  event.  When  we 
say,  then,  that  any  event  is  undesirable,  we  make  ab- 
straction of  future  compensations.  All  disservices  are 
"necessary  evils";  they  lead  to  good,  but  are  themselves 
evils. 

We  have,  then,  the  following  account :  — 

INCOME  FOR  HOUSE  AND  LOT  DURING  YEAR  1901 
Income  Outgo 

Use  of  house  and  lot  (six  Expense     of     building 

months) $600          house SI  0,000 

Taxes  100 


$600  $10,100 

During  this  year,  then,  the  house  yields  a  net  outgo  of  S9500. 
This  adverse  balance  will  be  more  than  made  up  in  the  years 
which  follow.  For  the  year  1902  we  may  have  the  fol- 
lowing :  — 

puts  fertilizers  on  his  land,  this,  his  outgo,  is  the  farm's  ingo.  But, 
although  we  shall  be  largely  concerned  with  income  and  outgo  in 
relation  to  capital  as  their  source,  and  might  therefore  logically 
employ  the  terms  outcome  and  ingo,  it  seems  preferable,  for  reasons 
of  usage,  to  retain  the  usual  terms,  income  and  outgo. 


124  NATURE   OF   CAPITAL   AND   INCOME          [CHAP.  VIII 

INCOME  FOR  HOUSE  AND  LOT  DURING  YEAR  1902 
Income  Outgo 

Use        $1200     Repairs $  50 

Taxes  150 


$1200  $200 


Net  income         ....     $1000 

Let  us  suppose  that  these  figures  remain  about  the  same 
for  forty-nine  years,  and  give  $50,000  net  income  dur- 
ing that  time,  which  cancels  the  excess  in  cost  for  1901 
of  $9500  and  leaves  a  large  margin  besides,  the  nature 
of  which,  as  interest,  need  not  here  be  considered.  Then  a 
second  time  the  house  is  worn  out  and  has  to  be  rebuilt. 
The  same  cycle  is  repeated,  one  year  of  excess  of  cost  being 
offset  by  forty-nine  years  of  excess  of  income. 

§3 

It  will  be  observed  that  the  cost  of  reconstructing  the 
house  was  entered  in  the  accounts  in  exactly  the  same  way 
as  repairs  or  other  "current"  costs.  There  may  seem  to 
be  objection  to  such  a  proceeding  in  the  thought  that  recon- 
struction appears  to  be  not  a  part  of  " running  expense" 
but  a  "capital  cost,"  and  belongs,  not  to  income  accounts, 
but  to  capital  accounts.  It  is  true  that  the  value  of  the 
new  house  must  be  entered  on  the  capital  balance  sheet, 
but  the  cost  of  producing  it  belongs  properly  to  income 
accounts.  The  former  represents  wealth;  the  latter  repre- 
sents disservices.  The  former  relates  to  an  instant  of  time 
(which  may  be  any  instant  from  the  time  it  is  begun  till 
the  time  when  it  ceases  to  exist) ;  the  latter  relates  to  a 
period  of  time  (which  may  be  all  or  any  part  of  the  time 
during  which  the  labor  and  other  sacrifices  occasioned  by 
the  house  occur).  A  house  is  quite  distinct  from  the 
scries  of  sacrifices  by  which  it  was  fashioned.  The  con- 
fusion between  the  two  is  natural  in  view  of  the  practice 


SEC.  3]  INCOME   ACCOUNTS  125 

of  bookkeepers  in  often  entering  capital  at  its  "cost  value." 
In  fact  it  is  sometimes  said  that  "liabilities  represent  money 
received  by  a  company,  and  assets,  how  it  has  been  ex- 
pended." But  this  is  not  strictly  true.  Since  its  market 
value  depends  on  its  suitability  to  the  uses  to  which  it  is 
put,  not  on  the  money  sunk  in  its  construction,  the  house  on 
which  was  expended  $10,000  for  construction  may  be  worth 
more  or  less  than  $10,000.  In  this  case  the  income 
account  should  contain  $10,000  on  the  outgo  side,  and 
the  capital  account  should  contain  a  larger  or  smaller 
figure.1 

And  yet  it  is  undoubtedly  true  that  we  instinctively 
object  to  entering  the  cost  of  building  the  house  in  its 
income-and-outgo  account;  and  we  express  this  objection 
by  calling  this  cost  a  "capital  cost,"  rather  than  a  part  of 
running  expenses.  By  so  classing  it  we  mean  that  it  does 
not  recur,  or,  at  any  rate,  only  at  long  intervals.  On  this 
basis  Wagner  and  others  have  erroneously  claimed  that 
income  and  outgo  should  be  confined  to  "regular"  items. 
At  first  glance  this  seems  feasible  because,  in  actual  prac- 
tice, an  extraordinary  expense  in  a  given  year,  like  the 
cost  of  constructing  a  house,  does  not  usually  reduce  the 
owner's  net  income  for  that  year  by  that  amount.  He  will 
generally  contrive  to  avoid  such  a  result  by  offsetting 
the  extraordinary  expense  of  the  house  by  a  correspond- 
ingly extraordinary  income  from  some  other  source,  such 
as  a  depreciation  fund.  It  is  evident  that  the  house  owner 

1  Even  in  the  normal  case  the  value  of  the  house,  as  is  well  known, 
is  not  exactly  equal  to  the  cost  expended  in  construction,  but  to  that 
amount  phis  interest.  A  house  which  costs  SI 0,000,  expended  through 
six  months,  ought  to  be  worth  a  few  hundred  dollars  more  than  this 
sum  at  the  time  of  completion ;  otherwise  the  man  who  expended  those 
$10,000,  and  at  completion  has  only  $10,000  worth  of  house  to  show 
for  it,  has  evidently  received  no  interest  on  his  money.  The  relation 
between  the  value  of  capital,  and  its  cost,  and  interest,  will  form  a 
subject  to  be  taken  up  in  a  later  chapter,  where  the  common  error 
that  accrued,  but  unpaid,  interest  is  itself  a  cost  will  also  be  dis- 
cussed. 


126  NATURE   OF   CAPITAL   AND   INCOME      [CHAP.  VIII 

who  has  had  the  foresight  to  set  aside  annually  throughout 
the  period  of  existence  of  the  house  a  small  deposit  in  a 
savings  bank,  may  derive  therefrom,  when  the  time  for 
rebuilding  arrives,  a  large  sum  of  money,  the  receipt  of 
which  is  just  as  properly  an  element  of  income  as  its 
expenditure  for  rebuilding  is  an  element  of  outgo.  The 
great  outgo  for  rebuilding  is  then  offset  by  a  great  income 
from  the  savings  bank  account,  so  that  the  combined  net 
income  from  the  two  sources  —  depreciation  fund  and 
house  —  will  be  approximately  zero  and  the  total  net  in- 
come of  the  individual  will  be  affected  little  or  not  at  all. 
The  depreciation  fund,  therefore,  does  not  prevent,  but 
merely  offsets  the  large  negative  balance  in  the  income 
account  from  the  "house  and  lot"  considered  by  itself. 
The  combined  income  from  the  two  sources  taken  together 
will  be  negligible,  but  that  from  the  one  source,  the  "  house 
and  lot,"  will  fluctuate.  In  figures,  from  this  single  source, 
the  net  income  is  evidently  +$1000  a  year  for  each  of  forty- 
nine  years,  and  —$9500  for  the  fiftieth  year.  It  is  mislead- 
ing to  say  that  the  $1000  is  "gross  "  income  from  which  must 
be  deducted  the  depreciation  fund  or  "amortization"  sup- 
posed to  be  laid  aside  each  year  against  the  cost  of  rebuild- 
ing. Merely  to  suppose  a  depreciation  fund  is  not  to  have 
one.  It  is  quite  true  that  the  $1000  income  which  the  house 
yields  during  each  of  forty-nine  years  is  more  than  the  income 
which  would  have  been  left  after  an  annual  payment  into 
a  depreciation  fund  had  actually  been  made ;  but  an  income 
which  simply  might  have  been  is  only  an  ideal  standard. 
Confusing  the  actual  and  the  ideal  is  one  of  the  commonest 
fallacies  in  this  field.  The  actual  net  income  of  the  house 
and  lot  is  alone  the  object  of  our  present  study,  and  this 
actual  income,  in  the  example  we  are  supposing,  is  $1000 
each  year  for  forty-nine  years.  While  this  sum  is  in  excess 
of  the  ideal  standard  income  during  each  of  these  forty- 
nine  years,  this  overplus  is  atoned  for  by  the  sudden  and 
large  deficiency  every  fiftieth  year. 


SEC.  4]  INCOME   ACCOUNTS  127 

§4 

Such  irregularity  of  income  may  be  avoided,  not  only 
by  a  depreciation  fund,  but  by  other  devices,  for  instance, 
by  paying  for  the  house  in  installments,  by  borrowing 
money  to  defray  cost  and  mortgaging  the  house,  or  by  sell- 
ing other  property.  Another  method  of  steadying  income 

—  and  one  which  ought  to  set  at  rest  any  remaining  qualms 
which  the  reader  may  feel  at  the  procedure,  which  has  been 
adopted,  of  entering  cost  of  new  construction  under  "outgo" 

—  applies  when  the  same  owner  possesses  so  many  of  the 
articles  in  question  that  the  reconstruction  of  one  or  another 
of  them  must  occur  at  short  intervals.     Consider,  for  in- 
stance, the  case  of  a  building  and  loan  association  which 
has  fifty  houses,  each  built  in   a  different  year  and  each  of 
which   lasts  fifty  years,  so   that   the  houses  have  to   be 
rebuilt  at  the  rate  of  one  every  year.     In  the  accounts  of 
such  an  association  the  expense  side  should  include  the 
cost  of  new  construction  as  a  regular  annual  item,  thus :  — 

BUILDING  AND  LOAN  ASSOCIATION 

Fifty  houses  (with  land)  1900 
Income  Outgo 

Rents  of  49  houses  at  Construction  of  one  new 

$1000  a  year     .     .     .     $49,000         house $10,000 

Rent  of    one    house  for  Repairs  on  49  houses  .         4,900 

part   of    the    year    in  Taxes          5,000 

which  it  is  constructed  500 


$49,500  $19,900 


Net  income      ....     829,600 

We  have  here  a  net  annual  income  of  $29,600,  which  con- 
tinues year  after  year  without  interruption.  The  irregu- 
larity of  income  which  we  found  in  the  case  of  a  single  house 
ceases  when  the  larger  number  is  taken.  But  if  it  is  proper 
to  regard  the  cost  of  reconstructing  the  houses  as  outgo 
in  the  case  of  a  large  number  of  houses,  it  must  be  equally 


128  NATURE    OF    CAPITAL   AND   INCOME       [CHAP.  VIII 

proper  to  regard  it  as  outgo  in  the  case  of  each  single  house ; 
for  the  income  account  of  the  total  mass  of  the  commu- 
nity's capital  is  simply  the  combined  accounts  of  the 
individual  elements.  We  cannot  consistently  do  other- 
wise than  regard  all  costs,  whether  recurrent  or  not,  as 
outgo. 

In  actual  business  there  are  usually  many  articles  of 
the  same  kind,  so  that  it  is  seldom  necessary  to  reckon  the 
net  income  from  each  individual  article.  Such  articles  may 
be  conveniently  lumped  together.  This  we  have  just  seen 
in  the  case  of  the  houses  of  the  loan  association.  As  an- 
other example  we  may  take  the  stock-in-trade  of  a  mer- 
chant. This  stock  yields  him  income,  not,  as  in  the  case 
of  the  house,  by  rent,  but  by  sale;  the  difference  between 
rent  and  sale  being  simply  that  rent  consists  of  a  series  of 
contributions  to  income,  whereas  sale  consists  only  of  one. 
A  stock  of  stoves,  just  as  a  stock  of  houses,  yields  income 
which  is  the  sum  of  the  net  incomes  from  its  individual 
constituents.  But  the  stove  dealer  would  find  the  book- 
keeping very  troublesome  were  he  to  reckon  in  a  separate 
account  the  net  income  from  each  individual  stove  which 
he  buys  and  sells.  He  reaches  the  same  final  result  for 
his  stock  as  a  whole  (or  rather,  for  each  specific  category 
of  articles  in  his  stock)  by  taking  from  his  gross  receipts 
obtained  by  selling  stoves  the  year's  cost  of  replenishing 
his  stock,  the  rent  of  his  warehouse,  salaries  of  clerks,  and 
other  outgo.  Were  he  to  arrive  at  this  result  by  applying 
the  same  process  to  each  individual  stove,  the  individual 
results  would,  of  course,  vary  widely ;  for  a  stove  left  over 
from  last  year  (and  therefore  free  from  any  item  of  cost 
in  this  year's  accounts),  if  sold  this  year,  would  give  a 
large  net  income,  while  another  stove,  bought  this  year, 
but  not  sold  until  next,  would  only  have  debit  items  in 
this  year's  account.  But  the  sum  of  these  irregular 
incomes  from  individual  parts  of  the  merchant's  stock 
will  give  a  steady  income  for  the  whole. 


SEC.  5]  INCOME   ACCOUNTS  129 

Any  merchant's  stock  that  rapidly  changes  the  individual 
elements  of  which  it  is  constituted  is  most  conveniently 
treated  as  a  whole.  To  use  Professor  Clark's  admirable 
simile,  it  is  like  Niagara  Falls,  which  remains  a  waterfall, 
although  consisting  each  day  of  entirely  different  drops  of 
water.  The  stock  of  a  butcher,  grocer,  or  fruiterer  consists 
of  rapidly  changing  elements,  but  remains  as  a  whole 
relatively  unchanged.  Though  it  would  be  logically  sound, 
it  wouid  be  foolish  and  impracticable  to  keep  an  income 
and  outgo  account  for  each  individual  leg  of  mutton  or 
box  of  figs.  The  tendency  to-day,  however,  is  distinctly 
toward  a  more  detailed  accounting.  Some  business  firms, 
by  means  of  modern  card  indices,  keep  a  careful  record  for 
each  separate  wriety  of  commodity  dealt  with,  if  not  for 
each  individual  article  in  that  variety.  The  important 
thing  to  observe  is  that  the  net  income  of  the  entire  group 
is  simply  the  difference  between  the  sums  of  the  incomes 
and  outgoes  of  the  elementary  units  which  constitute  that 
group.  The  very  item  which,  for  the  elementary  unit, 
constitutes  "capital"  cost,  and  which,  for  that  unit,  occurs 
but  once,  becomes,  for  the  group,  the  regular  cost  of  re- 
plenishing, and  recurs  annually.  From  the  explanations 
and  illustrations  which  have  been  given,  it  is  clear  that 
consistency  and  logic  must  assign  to  every  cost,  whether 
large  or  small,  regular  or  irregular,  a  place  as  an  element  of 
outgo  in  the  income-and-outgo  accounts. 

§5 

Whether  or  not  the  irregularities  of  income  from  indi- 
vidual articles  of  wealth  are  smoothed  away  in  the  total, 
the  combined  income,  even  from  a  large  group  of  articles, 
is  not  necessarily  an  absolutely  steady  flow.  We  usually 
strive  to  make  it  so  to  some  extent ;  but  we  do  not  always 
succeed,  nor  do  we  even  always  try.  When  income  does 
vary,  the  method  of  measuring  which  has  been  given  will 
unerringly  register  that  variation  automatically.  The 


130  NATURE    OF    CAPITAL    AND    INCOME      [CHAP.  VIII 

method  is  not,  of  course,  restricted  to  a  group  of  articles 
of  the  same  kind,  like  the  fifty  houses  of  the  building  and 
loan  association  or  the  stock  of  stoves,  of  the  stove  dealer 
It  applies  to  any  stock  of  miscellaneous  articles,  and  even 
to  the  entire  stock  of  wealth  of  a  community  or  the  wond. 
The  net  income  from  any  such  group  is  simply  the  sum  of 
the  net  incomes  of  the  various  articles  of  wealth  in  exist- 
ence at  all  the  points  of  time  within  the  period  for  which 
that  income  is  reckoned. 

In  like  manner  may  be  obtained  the  income  from  any 
collection  of  property  rights  as  capital.  This  application 
of  income-and-outgo  accounts  occurs  especially  in  the  case 
of  an  individual.  For  we  then  find  that  the  sources  of 
income  consist  largely,  not  of  capital-wealth,  but  of  capi- 
tal-property,—  partial  rights  to  wealth,  such  as  bonds, 
stocks,  and  mortgages.  But  the  introduction  of  the  idea 
of  property  as  distinct  from  that  of  wealth  involves  no  new 
difficulties ;  for  we  have  seen  that  property  is  only  another 
aspect  of  wealth,  and  represents  simply  rights  to  some  of 
the  services  of  wealth.  Thus  in  respect  to  partnership 
rights,  each  partner  in  the  firm  of  Smith  &  Jones,  farmers, 
receives  half  the  income  of  the  farm.  The  same  principle 
applies  in  respect  to  shares,  bonds,  or  other  forms  of  prop- 
erty. Business  men  are  accustomed  to  say  that  a  railway 
bond  yields  or  earns  so  much  income.  But  this  merely 
means  that  the  railway  behind  this  bond  yields  income,  a 
specified  share  of  which  belongs  to  the  bondholder.  Thus 
the  true  source  of  the  services  which  flow  to  the  property 
holder  is  the  concrete  wealth;  his  property-right  merely 
specifies  such  portion  of  those  services  as  are  his.  The 
income  of  a  stockholder,  for  instance,  consists  of  all  the 
benefits  he  receives  from  being  a  stockholder,  less  all  the 
sacrifices.  Usually,  for  him,  both  benefits  and  sacrifices 
accrue  in  monetary  form.  His  income  from  his  stock  is 
usually  the  receipt  of  dividends. 

The  total  net  income  of  a  person  is,  then,  the  sum  of 


SEC.  6]  INCOME   ACCOUNTS  131 

the  net  incomes  from  each  individual  article  of  property 
which  he  holds  within  the  time  interval  considered. 

§6 

To  illustrate  this,  let  us  consider  the  case  of  a  lawyer 
living  in  a  rented  house,  but  owning  the  furniture.  We 
shall  assume,  for  simplicity,  that  his  property  is  grouped 
under  the  following  nine  heads:  (1)  stocks  and  bonds, 
(2)  lease  of  house  (including  not  only  the  privilege  of  occu- 
pancy but  also  the  obligation  to  pay  rent),  (3)  furniture 
of  house,  (4)  other  household  supplies,  especially  food, 
(5)  money  and  bank  account,  (6)  claim  on  servants  (includ- 
ing not  only  the  claim  on  their  work  but  also  the  obligation 
to  pay  wages),  (7)  like  claims  on,  coupled  with  obligations 
from,  office  clerks,  (8)  his  own  person,  (9)  "  etc."  We 
shall  take,  as  the  time  interval,  a  period  of  a  month. 

During  the  month,  the  stocks  and  bonds  bring  in  checks 
aggregating  $2,000  and  the  lawyer  buys  new  securities  to 
the  extent  of  $500.  His  total  net  income,  therefore,  dur- 
ing this  particular  month  from  this  particular  group  of 
property  rights  is  $1500.  Under  his  lease  he  enjoys  a 
month's  use  of  a  house,  this  use  being  regarded  by  him  as 
worth,  let  us  say,  exactly  what  it  costs,  or  $100  a  month. 
Since  the  lease  yields  him  $100  worth  of  shelter  and  costs 
him  $100  in  money,  it  leaves  no  net  income.  His  furni- 
ture yields  him  comfort  worth  $50,  from  which  cost  of 
repairs,  etc.,  amounting  to  $30,  has  to  be  deducted,  leav- 
ing a  balance  of  $20.  His  stock  of  food  and  similar  sup- 
plies yields  him  the  board  of  himself  and  family  for  the 
month,  worth  $150 ;  but  the  cost  of  replenishing  this  stock 
and  the  services  of  cook  and  waitress  in  preparing  and 
serving  it  absorb,  let  us  say,  all  of  this  sum,  leaving  for 
the  month  no  net  income  from  the  pantry's  stock. 

The  next  source  of  income  (or  outgo)  is  "  cash."  By 
this  is  meant  the  stock  of  property  which  includes  money 
on  hand  and  money  on  deposit  in  bank.  To  find  how 


132  NATURE    OF    CAPITAL   AND    INCOME      [CHAP.  VIH 

much  income  or  outgo  comes  from  "  cash  "  we  need  only 
follow  the  well-established  usage  of  bookkeepers  which 
regards  a  stock  of  cash  as  though  it  were  a  gold  mine 
which,  consequently,  is  to  be  credited  with  all  the  gold  or 
cash  which  comes  out  of  it,  and  debited  with  all  that  goes 
into  it.  This  usage  often  puzzles  the  novice,  but  its  cor- 
rectness is  undoubted  and  it  harmonizes  with  our  defini- 
tion of  services  and  disservices.  For  the  services  or 
desirable  events  which  come  from  one's  stock  of  cash  - 
the  events,  in  fact,  for  the  sake  of  which  that  stock  of 
cash  exists  —  are  the  furnishing  of  money  from  time  to 
time ;  the  disservices,  or  the  undesirable  events  occasioned 
by  that  stock  of  cash,  are  the  absorption  by  it  of  money 
from  time  to  time.  In  other  words,  my  purse  serves  me 
whenever  it  pays  my  bills ;  it  costs  me  whenever  I,  so  to 
speak,  pay  its  bills.  In  this  respect  it  is  precisely  similar 
to  any  other  stock  of  wealth.  A  bin  of  coal  serves  its  owner 
when  it  renders  him  fuel;  it  costs  him  when  it  has  to  be 
filled.  The  cost  may  be  the  sacrifice  of  money,  of  labor,  or 
of  coal  taken  from  some  other  store  of  coal.  In  the  case 
before  us,  the  income  from  "cash,"  or  all  the  payments  the 
lawyer  takes  out  of  his  pocket-book  or  check  book,  amounts, 
let  us  say,  to  $3780,  whereas  the  outgo  to  "cash"  -all 
sums  paid  to  it  —  amounts  to  $4000,  leaving  $220  as  a 
net  outgo. 

The  claim  on  the  servants,  like  the  lease  of  the  house, 
involves  an  obligation  to  pay  as  well  as  a  right  to  receive. 
We  shall  suppose  that  the  servants  render  services  during 
the  month  worth  $100,  and  also  cost  $100  in  wages,  leav- 
ing no  net  balance.  Similarly  the  office  clerks  cost  $500 
in  wages  and  yield  $500  worth  of  assistance  to  the  lawyer 
in  the  preparation  of  his  cases. 

The  man  himself  receives  from  his  practice  during  the 
month  $2000.  But  his  office  and  professional  expenses 
amount  to  $500  and  leave  a  balance  of  $1500.  The  class 
called  "etc."  comprises  all  sources  of  income  not  other- 


SKC.  6] 


INCOME   ACCOUNTS 


wise  included,  such  as  clothing,  watches,  jewelry,  and  other 
articles  of  wealth  or  property  not  contained  in  the  other 
categories.  For  simplicity  we  shall  suppose  that  the  in- 
come and  outgo  connected  with  "  etc."  are  equal  to  each 
other,  and  amount  to  $2500. 

The  total  income  of  this  man  is  therefore  as  follows :  — 


Income 


Outgo 


Income 


I'rotit  and 

Loss 

By  stocks  and  bonds 

To  stocks  and  bonds 

(money)     .... 

S2000 

(money)  $  500 

+  SI  500 

By  lease  right  (shelter) 

100 

To  lease  right  (money)      100 

00 

By  furniture  (use)  .     . 

50 

To  furniture  (money)        30 

+         20 

To  food  (money  (50) 

and  work  of   serv- 

By food  (use)       .     .     . 

150 

ants  (100)  ....      150 

00 

By  "  cash  "  (money)    . 

3780 

To  "  cash  "  (money)  .    4000 

-       220 

By  servants  (services) 

100 

To   servants  (money)      100 

00 

By  clerks  (personal  as- 

sistance)     .... 

500 

To  clerks  (money)  .     .      500 

00 

To  self  (assistance  of 

By  self  (money) 

2000 

clerks)  (money)      .      500 

+     1500 

By  "etc."  (direct  uses) 

2500 

To  "etc."  (money)      .    2500 

00 

Total  net  income   . 

+  S2800 

These  accounts  may  be  simplified  in  various  ways,  and 
without  any  sacrifice  of  logical  completeness.  If  we  are 
interested  only  in  the  total  net  income,  and  not  in  the  share 
which  each  item  of  property  contributes  to  this  total,  we 
may  omit  several  items  which  in  the  above  accounting  stand 
on  both  sides.  For  instance,  the  cooking  and  serving  food 
was  debited  to  the  stock  of  food  and  credited  to  the  servants. 
At  first  sight  it  may  appear  that  the  wages  of  cook  and 
waitress  are  entered  as  debit  both  to  "servants"  and  to 
"food"  and  that  double  counting  has  occurred.  But  the 
debit  to  food  was  not  servants'  wages  but  servants'  work. 


134  NATURE    OF    CAPITAL   AND    INCOME      [CHAP.  VIII 

A  little  consideration  will  show  that  if  we  credit  the  servants 
with  the  services  of  cooking  and  waiting,  and  debit  them 
with  wages  as  a  distinct  item,  we  must  debit  the  food 
with  their  services  of  cooking  and  waiting.  If  we  prefer 
to  drop  out  these  services  both  from  the  credit  side  of  the 
servants'  account  and  the  debit  side  of  the  food  account, 
we  are  then  at  liberty  to  omit  the  category  of  servants 
entirely,  and  to  leave  only  the  charge  of  their  wages 
against  the  food.  There  are  endless  admissible  modifica- 
tions of  the  accounting  here  described,  many  of  wThich 
have  practical  advantages,  but  the  preceding  is  pre- 
sented as  a  complete  and  detailed  record  of  all  income  and 
outgo  arranged  by  sources. 

§7 

In  complete  accounting  we  must  not  omit  the  negative 
items  of  property,  or  liabilities.  The  same  principles 
apply  here  as  for  positive  items,  or  assets.  Items  which 
are  negative  are  such  because  they  yield  negative  income, 
or  outgo.  If  the  lawyer  whose  accounts  we  have  followed 
is  in  debt,  the  payments  on  his  debt  (whether  "interest" 
or  "principal")  which  he  makes  during  the  time-interval 
considered  are  outgo.  On  the  other  hand,  if  a  debt  is 
contracted  during  the  time-interval  considered,  its  pro- 
ceeds are  for  that  period  an  addition  to  gross  income. 

Thus  an  income-and-outgo  account  may  always  be  com- 
pletely formed  by  recording  the  values  of  the  services  and 
disservices  occasioned  by  all  the  articles  of  capital  under 
consideration.  In  the  case  of  an  individual  these  articles 
of  capital  are  his  assets  and  his  liabilities.  No  other  items 
than  the  services  and  disservices  mentioned  can  properly 
find  a  place  in  the  accounts.  We  have  already  warned 
the  reader  against  the  fallacy  of  deducting  from  income 
any  depletion  of  capital;  he  should  also  be  warned 
against  the  opposite  fallacy  of  adding  to  income  any  sav- 
ings of  capital.  This  fallacy  is  so  common  and  so  subtle 


SEC.  8]  INCOME   ACCOUNTS  135 

that  its  discussion  will  be  postponed  to  Chapter  XIV, 
where  it  may  receive  the  attention  it  deserves.  We  con- 
tent ourselves  at  present  with  a  preliminary  illustration. 
A  savings  bank  depositor  is  sometimes  thought  to  draw 
income  from  his  deposit  when  the  interest  "accumulates." 
This  is  an  error.  He  draws  income  when,  and  only  when, 
he  draws  money  out  of  the  bank ;  he  suffers  outgo  when, 
and  only  when,  he  puts  money  into  it.  If  he  merely  lets 
his  deposit  accumulate,  he  derives  no  income  and  suffers 
no  outgo.  There  is  no  effect  on  income.  What  does  occur 
is  increase  of  capital.  He  cannot  have  his  cake  and  eat  it 
too.  If  we  make  the  fiction  that  the  man  who  allows  his 
savings  to  accumulate  virtually  receives  the  interest,  we 
must,  to  be  consistent,  also  make  the  fiction  that  he  rede- 
posits  it.  If  the  teller  hands  over  the  interest  across  the 
counter,  the  depositor's  account  certainly  yields  up  "in- 
come" to  him,  but  if  he  hands  it  back  it  must,  in  consist- 
ency, be  charged  as  "outgo,"  and  the  net  result  on  his 
income  is  simply  a  cancellation.  This  procedure  reveals 
clearly  the  fact  that  the  accumulation  is  not  income. 


The  method  of  accounting  employed  in  the  preceding 
lawyer's  account  is,  of  course,  not  the  only,  nor  is  it  the 
usual,  method.  It  is  the  method,  however,  which  shows 
the  shares  of  the  total  income  attributable  to  each  indi- 
vidual source.  In  practice,  the  minor  sources  of  income 
are  neglected.  The  income  and  outgo  of  one's  "cash" 
almost  balance  in  the  long  run,  and  the  same  is  true  of 
the  lease,  the  servants'  contracts,  and  the  household  sup- 
plies. One's  furniture  probably  yields  a  larger  net  income 
than  is  commonly  realized,  but  even  this  is  usually  a  small 
element  in  the  total.  It  is  only  in  case  the  lawyer  lives  in 
hisown  house  that  a  serious  correction  would  need  tobe  made 
on  this  account.  In  this  case,  his  shelter  is  not  offset  by 
any  rent  payment,  and  enters  the  accounts  as  pure  income. 


136  NATURE    OF    CAPITAL    AND    INCOME      [CHAP.  VIII 

Practically,  therefore,  the  lawyer's  income  is  obtained 
by  taking  from  the  above  table  only  the  two  principal 
items,  the  income  from  investments  and  the  income  from 
his  professional  work.  Each  of  these  is  $1500,  so  that 
according  to  this  approximate  accounting  the  net  income 
is  $3000.  Another  and  more  common  method  of  approxi- 
mating an  income  account  is  to  record  simply  money 
receipts  and  disbursements,  in  other  words,  to  record 
only  the  items  of  the  preceding  account  under  "cash." 
The  lawyer's  cash  account  book  would  present  an  appear- 
ance like  the  following :  — 

Receipts 

From  stocks  and  bonds 
From  personal  labor    . 


$2000 
2000 

Disbursements 

Investments,     in     stocks 
and  bonds      .... 
Rent    

$  500 
100 

Furniture  repairs  . 
Cost  of  food       .... 
Servants   

30 
50 
100 

Clerk  hire      
"Etc." 

500 

2500 

$4000  $3780 

This  leaves  a  cash  balance  of  $220,  which  is  to  be  added, 
at  the  end  of  the  month,  to  the  cash  on  hand  at  the  begin- 
ning. This  balance  does  not  here  indicate  the  net  income 
of  the  lawyer,  as  did  the  balance  in  the  completer  account- 
ing which  preceded.  The  net  income  of  the  lawyer,  in  the 
incomplete  and  makeshift  accounting  now  under  consid- 
eration, is,  so  far  as  it  is  represented  at  all,  shown  in  the 
total  cash  receipts  less  certain  makeshift  corrections.  The 
justification  of  such  accounting,  so  far  as  any  exists,  is  that 
most  income,  from  whatever  source,  passes  through  the 
cash  drawer. 

It  will  be  noticed  that  the  receipts  side  of  the  above 
account,  $4000,  greatly  exceeds  the  true  net  income, 
$2800,  shown  in  the  previous  accounting.  Instinctively 
any  one  using  such  mere  money  accounting  feels  the  need 


SEC.  8]  INCOME    ACCOUNTS  137 

of  making  tome  deductions  from  the  total  money  receipts. 
He  also  instinctively  feels  that  not  all  of  the  disbursements 
should  be  thus  deducted;  otherwise  little  or  nothing  would 
remain.  The  ordinary  makeshift  is  to  deduct  the  "  business 
expenses,"  —the  $500  invested  in  stocks  and  bonds  and 
the  $500  for  clerk  hire.  The  remainder  will  then  be 
$3000,  which  is,  for  practical  purposes,  a  sufficiently  close 
approximation  to  the  true  net  income  of  $2800. 

Practically,  therefore,  either  money  receipts  (less  "busi- 
ness" expenses)  or  the  sum  of  the  net  incomes  from  secu- 
rities and  labor,  are  good  makeshifts  for  true  income.  But 
even  from  a  practical  point  of  view  they  will  not  always 
serve,  while  as  a  matter  of  strict  theory  they  are  always 
wrong.  They  could  be  right  only  under  the  condition  that 
all  income,  from  whatever  source,  flowed  through  the  cash 
drawer.  If  it  were  true  that  the  net  income  from  stocks  and 
bonds,  the  net  income  from  the  lawyer's  practice,  and,  in 
like  manner,  the  net  income  from  every  other  source  flowed 
into  the  cash  drawer,  while,  on  the  other  hand,  the  flow  out 
of  that  drawer  consisted  exclusively  of  expenditures  for 
each  and  every  satisfaction  as  it  occurred,  then  the  flow  of 
money  through  the  cash  drawer  would  serve  as  a  true  meas- 
ure of  income,  and  the  cash  drawer  might  be  called  a  sort  of 
income  meter.  The  flow  into  it  would  be  money  income 
and  the  eventual  satisfactions  obtained  from  it  would  be 
real  income.  The  two  would  then  also  have  the  relation 
usually  ascribed  to  them  by  economists.  This  case  is 
practically  realized  in  the  case  of  a  rentier,  who  simply  re- 
ceives money  from  investments  and  spends  it  for  imme- 
diate satisfactions,  renting,  let  us  say,  not  only  a  dwelling 
but  its  furniture  as  well,  so  that  practically  no  part  of  his 
income  can  reach  him  except  by  passing  through  the  money 
stage.  But  few  people  are  in  exactly  this  position,  so  that 
not  all  income  passes  through  the  meter.  Some  passes 
around  it,  as,  for  instance,  the  shelter  derived  from  a  man's 
own  house  or  the  comforts  from  his  own  furniture,  and  hence 


138  NATURE   OF    CAPITAL  AND   INCOME        [CHAP.  VIII 

will  not  be  registered  by  the  meter  at  all.  On  the  other 
hand,  some  passes  through  it  not  toward  direct  satisfactions 
but  toward  some  "business"  expenditure  likely  later  on  to 
repour  cash  through  the  money  meter  and  hence  to  cause 
it  to  register  too  much.  Thus  it  happens  that  the  money 
meter  sometimes  fails  to  register  and  sometimes  registers 
twice.  It  is  therefore  only  a  rough  and  imperfect  instru- 
ment for  measuring  net  income. 

§9 

When  we  turn  from  real  to  fictitious  persons,  we  find,  for 
income  accounts,  as  for  capital  accounts,  that  the  two  sides 
necessarily  balance  exactly.  A  corporation,  as  an  entity 
distinct  from  its  stockholders,  cannot  enjoy  income  or 
suffer  outgo.  All  the  income  not  devoted  to  other  ex- 
penses is  absorbed  in  paying  dividends.  A  railway  com- 
pany, for  instance,  has  an  income  account  as  follows:  — 

INCOME  ACCOUNT  OF  RAILROAD  CORPORATION  FOR  YEAR 
Income  Outgo 

By     passenger     and                            To       operating        ex- 
freight  service       .     $1,246,147         penses $800,000 

To    interest    to    bond- 
holders        ....     100,000 
To  dividends  to  stock- 
holders   200,000 

To  surplus  applied  to 

(1)  purchase     of 

land          ....     140.000 

(2)  cash  in  treasury         6,147 


$1,246,147  $1,246,147 

In  these  accounts  we  see  that  the  gross  income  from  all 
sources  was  $1,246,147,  of  which  S800,000  disappeared  for 
running  expenses,  $100,000  for  paying  bondholders,  and 
$200,000  for  paying  stockholders,  leaving  a  balancing  item 
of  $146,147.  But  this  balance  is  likewise  expended,  $140,- 
000  of  it  being  outgo  for  new  land,  and  the  small  odd  sum 


SEC.  10]  INCOME   ACCOUNTS  139 

$6147  being  put  into  the  safes  of  the  company  or  deposited 
in  bank.  Even  this  last  operation  is  a  true  outgo;  for  a 
cash  drawer  and  a  bank  account  are,  as  we  have  seen,  always 
debited  with  what  is  put  into  them.  There  remains,  there- 
fore, no  final  balance  for  the  abstraction  called  the  "  com- 
pany." Just  as,  in  the  capital  accounts,  the  company's 
excess  of  assets  over  liabilities  to  other  than  stockholders 
constitutes  the  true  liability  to  the  stockholders  themselves, 
so,  in  income  accounts,  any  excess  of  income  over  outgo  to 
other  purposes  than  dividends  paid  to  stockholders  con- 
stitutes a  true  outgo  for  the  benefit  of  those  stockholders. 

§10 

We  see,  then,  that  the  guiding  principle  for  the  construc- 
tion of  the  income  account,  either  of  real  or  fictitious  per- 
sons, is  simply  to  make  a  complete  list  of  the  services  and 
disservices  which  flow  from  each  and  every  item  of  the  assets 
and  liabilities.  This  simple  relation  between  capital  and 
income  accounts  is  commonly  obscured  by  the  fact  that  it 
is  not  practically  convenient  to  include  in  one's  capital  ac- 
counts certain  items  of  assets  and  liabilities,  although  their 
services  and  disservices  are  entered  in  the  income  account. 
This  is  true,  in  particular,  of  one's  own  person,  and  such 
claims  as  are  coupled  with  equal  obligations,  as  leases  and 
contracts  with  laborers.  These  are  not  and,  from  a  purely 
practical  point  of  view,  ought  not  to  be  entered  in  the 
capital  account ;  but  much  of  the  income  and  outgo  from 
them,  such  as  wages  and  rent,  are  entered  in  the  income 
account.  In  respect  of  income  accounts  the  use  of  one's 
dwelling  is  omitted,  as  well  as  the  unpaid-for  services  and 
disservices  of  human  beings.  A  shopkeeper  usually  keeps 
a  punctilious  record  of  the  work  of  his  employees,  but  sel- 
dom any  of  his  own  personal  work.  If  he  owns  the  build- 
ing he  occupies,  he  will  not  usually  include  its  use  in  his 
accounts.  In  private  life  he  seldom  or  never  includes  in 
his  accounts  the  use  of  furniture. 


140  NATURE    OF    CAPITAL   AND    INCOME      [CHAP.  VIII 

Our  present  object,  however,  is  to  show,  not  the  methods 
of  practical  bookkeeping,  but  merely  the  application  of 
economic  principles  to  such  bookkeeping.  The  chief  ob- 
ject is  to  find  the  philosophical  basis  of  accounting.  Care- 
ful examination  shows  that  accounting  is  at  bottom  not  a 
mere  makeshift  but  a  complete,  consistent,  and  logical  sys- 
tem. When  thus  conceived  and  understood  it  will  be  seen 
to  be  of  importance,  not  alone  to  the  accountant  but  also  to 
the  economist.  For  his  purposes,  the  only  method  of  con- 
structing income  and  outgo  accounts  which  is  philosophic- 
ally correct,  and  which  can  serve  as  a  basis  for  economic 
analysis,  is  the  method  by  which  are  recorded,  for  each 
article  of  capital,  the  values  of  all  its  services  and  disserv- 
ices. These  services  and  disservices  are  of  many  kinds. 
Sometimes  they  consist  of  money  payments,  sometimes  of 
productive  operations,  and  sometimes  of  enjoyable  ele- 
ments. These  all  enter  the  accounts  on  the  same  footing, 
but  in  the  next  chapter  we  shall  see  that  after  being  thus 
entered,  the  items  may  be  so  combined  that  all  except  the 
enjoyable  elements  will  cancel  among  themselves. 


CHAPTER  IX 

INCOME    SUMMATION 


WE  have  now  seen  how  to  reckon  the  income  of  either  a 
real  or  a  fictitious  person.  By  combining  the  net  incomes 
of  all  persons,  the  net  income  of  society  may  be  obtained. 
As  we  have  seen,  fictitious  persons  have  no  net  income, 
and  would  therefore  not  affect  such  a  method  of  summation. 
Another  way  to  obtain  the  total  social  income  is  by  adding 
together  the  net  incomes  from  each  individual  article  of 
concrete  capital,  regardless  of  its  ownership.  In  such  a 
summation  no  partial  property-rights,  such  as  stocks  and 
bonds,  would  appear.  Instead  we  would  only  find  actual 
railways,  mills,  refineries,  and  other  concrete  capital.  For 
instance,  the  net  income  earned  by  the  Southern  Pacific 
Railroad,  considered  as  an  aggregate  of  roadbed,  termi- 
nals, rolling  stock,  and  other  existing  instruments,  would 
be  taken.  This  would  not  be  the  income  of  the  Southern 
Pacific  Railroad  Company,  for,  as  we  have  seen,  the  com- 
pany, as  such,  has  no  net  income.  Nor  would  it  be  the 
income  of  the  stockholders  of  the  company,  for  this  con- 
stitutes only  a  part  of  the  earnings  of  the  road.  Nor 
would  it  be  exactly  the  sum  of  the  incomes  of  the  stock- 
holders and  bondholders,  inasmuch  as  the  company  may 
earn  income  from  other  sources  than  the  railroad  itself,  as, 
for  instance,  through  leases  of  other  roads  and  shares  held 
in  other  companies,  none  of  which  income  is  produced  by 
the  railway.  It  would  be  simply  the  difference  between 
the  total  value  of  the  services  of  transportation  rendered 

141 


142  NATURE   OF   CAPITAL   AND   INCOME          [CHAP.  IX 

by  the  railroad  and  the  value  of  the  disservices  occasioned 
by  it,  whether  through  cost  of  operation,  repairs,  renewals, 
or  betterments. 

The  two  ways  of  obtaining  the  total  social  income  which 
have  just  been  outlined  —  (1)  by  summing  the  net  incomes 
of  individual  persons  as  owners,  and  (2)  by  summing  the  net 
incomes  from  individual  articles  of  wealth  as  sources — may 
be  illustrated  by  supposing  two  ledgers  to  be  opened  con- 
taining the  income  for  a  given  community,  one  ledger 
being  devoted  to  each  way.  Each  page  of  Ledger  No.  1 
would  be  devoted  to  the  income-account  of  a  particular 
individual,  stating  in  detail,  in  two  columns,  the  items  of 
income  and  outgo  in  the  minute  manner  already  shown. 
In  Ledger  No.  2  likewise  each  page  would  be  devoted  to 
the  income-account  of  a  particular  article  of  wealth.  The 
first  ledger  would  represent,  therefore,  the  distribution  of 
income  among  different  persons  in  the  community.  The 
summary  of  such  a  ledger,  arranged  according  to  the  mag- 
nitude of  the  incomes,  would  give  us  the  "distribution 
curve"  of  incomes  shown  by  Professor  Pareto.1 

Let  us  suppose,  for  the  sake  of  illustration,  that  the  fol- 
lowing is  such  a  summary  for  the  United  States :  — 

DISTRIBUTION'  LEDGER  No.  1 

Net  Income  for  1900 

15,000  millionaire  families         $  2,000,000,000 

100,000  families,  incomes  ranging  from  310,000  to 

S50,000 3,000,000,000 

1,000,000  families,  incomes  S1000  to  $10,000  .  .  5,000,000,000 
20,000,000  families  below  $1000  10,000,000,000 


$20,000,000,000 

The  second  ledger  would  show  the  same  total  income, 
but  distributed  according  to  the  source  which  produced  it. 
We  may  suppose  a  summary  of  Ledger  No.  2  to  be  as 
follows :  — 

1  See  his  Cours  d'Economie  Politique,  Lausanne,  1897,  Vol.  II,  pp. 
299-345. 


SEC.  2]                                   INCOME    SUMMATION  143 

DISTRIBUTION  LEDGER  No.  2 

Net  Income  for  1900 

From  land $  2,000,000,000 

"      buildings 2,000,000,000 

"      railways  and  tramways 1,000,000,000 

"      factories 1,000,000,000 

"      persons 13,000,000,000 

"      etc 1,000,000,000 


$20,000,000,000 

§2 

Both  these  ledgers  would  be  constructed  by  combining  a 
number  of  separate  net  incomes,  each  one  of  which  was  the 
balance  remaining  after  deducting  the  outgo  from  the  gross 
income  of  the  particular  group  of  capital  considered.  In 
other  words,  both  ledgers  would  be  constructed  —  to  adopt 
the  phrase  which  was  employed  under  capital  accounts  — 
by  the  "method  of  balances." 

But  there  is  also  a  second  method  of  summing  incomes,  — 
the  "method  of  couples."  Just  as  the  same  item  in  capital 
accounts  is  both  asset  and  liability,  according  to  the  point  of 
view,  and  is,  therefore,  self-canceling,  so  the  same  item  in 
income  accounts  is  both  service  and  disservice,  and  is,  there- 
fore, also  self-canceling.  The  reader  may,  in  fact,  have  felt 
that,  in  many  of  the  examples  cited,  what  we  called  dis- 
services seemed  to  him  to  be  services.  He  may  have  asked 
himself,  Why  should  we  call  rebuilding  a  house  a  disservice  ? 
When  a  carpenter  and  his  tools  repair  it,  do  we  not  credit 
him  and  them  with  services?  Is  not  any  production  a 
service  ?  Are  not,  then,  repairs  placed  on  the  wrong  side 
of  the  ledger  ?  In  answer  it  may  be  said  that  when  a  car- 
penter with  his  plane,  hammer,  and  saw  helps  to  rebuild  a 
house,  we  have  to  consider  two  groups  of  capital.  One 
group,  the  carpenter  and  tools,  is  acting  on  the  other  group, 
the  house.  The  carpenter  and  tools  used  in  the  process 
certainly  perform  a  service,  but  the  house  does  not.  Con- 
sidered as  occasioned  by  the  house,  the  repairs  are  dis- 
services. The  house  absorbs  or  soaks  up  these  costs, 


144  NATURE   OF   CAPITAL   AND   INCOME  [CHAP.  IX 

promising  to  compensate  for  them  by  better  service  later 
on.  The  renailing  of  loose  shingles  is  certainly  not  what 
the  house  is  for,  but  is  only  a  necessary  evil.  On  the  part 
of  the  hammer,  however,  these  same  events  are  services. 
The  service  called  "nailing"  is  credited  to  the  hammer. 
Therefore  the  repairing  of  the  house  is  at  once  a  service 
and  a  disservice. 

Such  double-faced  events  require  a  special  name.  We 
may  christen  them  interactions  between  two  instruments 
or  groups  of  instruments.  Alternative  names  are  inter- 
acting services,  intermediate,  or  preparatory  services, 
coupled  services,  or  simply  "couples."  They  underlie 
what  business  men  call  "double  entry  bookkeeping." 

An  interaction,  then,  is  a  service  of  the  acting  instrument, 
a  disservice  of  the  instrument  acted  on.  There  can  never 
arise  the  slightest  doubt  as  to  when  it  is  to  be  regarded  as 
positive  and  when  negative.  The  definitions  of  service  and 
disservice  settle  this  question  in  each  case,  by  referring  it 
to  the  desire  of  a  human  being,  viz.  the  owner  of  the  service 
or  disservice.  As  he  desires  that  the  house  should  not  occa- 
sion repairs,  these  repairs  are  disservices  of  the  house;  as 
he  desires  that  the  tools  should  occasion  repairs,  they  are 
services  of  those  tools.  The  hammer  exists  for  and  derives 
its  value  from  its  prospective  services  in  renailing  shingles. 
The  house  does  not  exist  for  nor  derive  its  value  from  the 
renailing  of  its  shingles;  on  the  contrary,  the  prospect  of 
that  event  detracts  from  its  value. 

The  example  given  is  typical  of  the  general  relations 
between  interacting  instruments.  The  mental  picture  we 
should  construct  is  that  of  two  distinct  groups  of  capital. 
Group  A  acts  on  group  B  for  the  benefit  of  the  latter. 
Whatever  the  nature  of  this  interaction,  A  is  credited  with  it 
and  B  debited.  The  credit  and  debit  are  equal  and  simul- 
taneous, the  only  result  of  the  interaction  being  that,  in 
consequence  of  it,  B  is  enabled  at  some  later  time  to  yield 
more  income. 


SEC.  3]  INCOME   SUMMATION  145 

Interactions  arc  essentially  identical  with  what  were  dis- 
cussed a  generation  ago  under  the  title  "  productive  serv- 
ices." But  inasmuch  as  the  name  "productive  services" 
is  not  a  very  happy  one,  and  its  use  has  been  so  confused  and 
has  engendered  so  many  verbal  quibbles,  it  seems  advisable 
not  to  revive  it.  The  essential  fact  that  these  "productive 
services"  were  two-faced  —  negative  as  well  as  positive  - 
was  always  overlooked,  and  there  remained  no  other  charac- 
teristic which  could  give  the  phrase  a  definite  and  scientific 
meaning. 

Interactions  constitute  the  great  majority  of  the  elements 
which  enter  into  income  and  outgo  accounts.  The  only 
services  which  are  not  merely  the  positive  side  of  interac- 
tions are  mental  satisfactions  —  desirable  conscious  experi- 
ences —  often  miscalled  "consumption";  and  the  only 
disservices  which  are  not  the  negative  side  of  interactions 
are  pains  or  "labor."  But  these  are  only  the  outer  fringes 
of  the  economic  fabric.  Between  them  is  a  connective  net- 
work of  productive  processes  and  commercial  transactions, 
every  fiber  of  which  has  two  sides,  a  positive  side  of  serv- 
ices and  a  negative  side  of  disservices. 


The  interactions  between  two  articles  or  groups  of  articles 
may,  of  course,  consist  either  in  causing  or  preventing 
changes  or  events.  The  events  or  changes  which  are 
caused  or  prevented  are  of  three  chief  kinds,  —  changes  of 
form  of  wealth,  changes  of  position,  and  changes  of  owner- 
ship ;  or,  transformation,  transportation,  and  transfer.  We 
shall  take  these  up  in  order. 

What  is  here  called  transformation  of  wealth  is  prac- 
tically identical  with  what  is  usually  understood  by  "pro- 
duction" or  "productive  processes."  *  By  the  transforma- 
tion of  wealth,  or  the  changes  produced  in  its  form,  is 
meant  the  changes  of  relative  position  of  its  parts.  Weav- 
1  Cf.  Marshall,  Principles  of  Economics,  3d  ed.,  p.  132. 


146  NATURE    OF    CAPITAL   AND   INCOME  [CHAP.  IX 

ing,  for  instance,  is  the  transformation  of  yarn  into  cloth 
by  a  rearrangement  in  the  relative  position  of  the  warp  and 
woof.  Spinning,  likewise,  consists  of  moving,  stretching, 
and  twisting  fibers  into  yarn ;  sewing,  of  changing  the  posi- 
tion of  thread  so  that  it  may  hold  cloth  together;  and  so 
with  carding,  wool-sorting,  shearing,  and  all  the  other 
operations  which  constitute  the  manufacture  of  fabrics. 

All  manufacture  and  agriculture  consist  simply  of  a 
series  of  transformations  of  wealth,  and  each  transformation 
is  two-faced.  On  the  part  of  the  transformed  instrument 
(or  instruments)  the  transformation  is  a  disservice ;  on  the 
part  of  the  transforming  instrument  (or  instruments)  it  is  a 
service.  We  have  seen  that  when  a  carpenter  and  his  tools 
transform  a  house,  i.e.  build  or  repair  it,  he  and  his  tools 
are  credited  and  the  house  is  debited.  The  same  is  true 
when  the  painter  decorates  it  or  the  janitor  cleans  it. 
When  a  cobbler  transforms  leather  into  shoes,  he  is  per- 
forming services;  the  shoes  at  each  stage  are  occasioning 
disservices,  or  costs.  When  a  bootblack  transforms  dirty 
shoes  into  clean  and  polished  ones,  he  likewise  is  rendering 
services,  and  the  shoes,  disservices.  In  like  manner,  a  loom 
which  produces  cloth  out  of  yarn  is  to  be  credited  with  this 
operation  as  income,  while  the  stock  of  cloth  receiving  the 
product  of  the  loom  is  to  be  debited  with  the  very  same  item 
as  part  of  its  outgo  or  "cost  of  production." 

Again,  land  renders  a  service  in  producing  wheat.  On 
the  part  of  the  wheat,  however,  this  is  a  disservice.  Wheat 
production  is  a  service  of  land,  a  disservice  of  wheat.  If 
we  consider  a  farm  as  pouring  its  crop  into  the  stock  of 
wheat  of  a  granary,  the  entry  of  wheat  from  farm  to  wheat 
stock  is  credited  to  the  farm  as  its  service  and  debited  to  the 
wheat  stock  as  its  disservice. 

Sometimes,  as  has  been  said,  the  interaction  consists  not 
in  causing  a  change,  but  in  preventing  one.  A  warehouse 
renders  its  service  as  a  means  of  storing  bales  of  cotton,  i.e. 
protecting  them  from  the  elements.  This  storage  is,  how- 


SEC.  3]  INCOME   SUMMATION  147 

ever,  on  the  part  of  the  stock  of  cotton,  an  element  of  outgo 
or  expense. 

As  has  already  been  intimated,  there  may  be,  and  usually 
are,  more  articles  than  one  in  either  or  both  of  the  two 
interacting  capitals.  Plowing,  or  the  transformation  of 
land  into  a  furrowed  form,  is  performed  by  a  plow,  a  horse, 
and  a  man.  The  plowing  is  a  cost  debited  to  the  land  on 
the  one  hand,  and  at  the  same  time  a  service  credited  to 
the  group  of  capital  consisting  of  the  plow,  horse,  and  man 
on  the  other.  We  are  not  here  concerned  with  the  problem 
of  how  much  should  be  placed  to  the  credit  of  each  co- 
operating agent,  but  merely  with  the  fact  that  the  sum 
total  of  the  three  is  equal  to  the  debit  for  the  land. 

The  principle  is  not  altered  if  one  or  more  of  the  trans- 
forming agents  perishes  and  another  comes  for  the  first  time 
into  existence  in  the  transformation.  Bread-baking  is  a 
transformation  debited  to  the  bread  and  credited  to  the 
cook,  the  range,  the  flour,  and  the  fuel,  of  which  the  last 
two  perish  as  soon  as  they  perform  their  services.  Agents 
which  disappear  in  the  transformation  but  reappear,  in 
whole  or  in  part,  in  the  product  are  called  "raw  materials." 
The  production  of  cloth  from  yarn  is  a  transformation  ef- 
fected by  means,  not  only  of  the  loom,  but  also  of  a  number 
of  other  agents,  and  among  them  the  yarn  itself.  The  cost 
of  weaving  includes  as  cost  the  consumption  of  raw  material, 
yarn,  and  this  consumption  of  yarn,  on  the  part  of  the 
yarn  itself,  is  not  cost  or  disservice,  but  service.  It  is 
the  event  for  which  the  yarn  had  existed.  When  cloth 
is  turned  into  clothes  this  transformation  is  a  service  to 
be  credited  to  the  cloth,  and  a  disservice  to  be  debited  to  the 
clothes.  All  raw  materials  yield  services  as  they  are  con- 
verted into  finished  products.  Their  conversion  is,  however, 
always  outgo  on  the  part  of  those  products. 

In  this  way,  when  an  article  passes  through  various  stages 
of  production,  it  is  often  an  arbitrary  matter  whether  we 
designate  those  stages  by  different  names  or  not.  A  "sap- 


148  NATURE   OF   CAPITAL    AND   INCOME  [CHAP.  IX 

ling"  grows  into  a  "tree."  We  may,  if  we  choose,  consider 
the  sapling  as  one  category  and  the  tree  as  another.  In 
this  case  the  "sapling"  performs  a  service  at  the  moment 
it  becomes  a  "tree,"  just  as  the  "tree"  performs  one  later 
when  it,  in  turn,  becomes  "lumber";  but  no  effect  on 
social  income  is  produced,  because,  if  we  credit  the  sapling 
with  the  value  of  the  tree,  we  must  debit  the  tree  with  the 
cost  of  the  sapling.  Likewise  we  may  arbitrarily  designate 
the  moment  when  a  "calf"  becomes  a  "cow,"  or  when 
"new"  wine  becomes  "old,"  without  disturbing  the  income 
accounts  of  society;  for  such  events  are  always  two-faced 
and  cancel  themselves  out  in  the  total.  We  may,  in  fact, 
mark  any  stage  whatever  in  the  course  of  production  by  an 
arbitrary  line,  and  regard  the  passage  across  this  line  as  a 
service  on  the  part  of  the  capital  on  one  side  of  the  line 
and  a  disservice  on  the  part  of  the  capital  on  the  other  side. 


The  second  class  of  interactions  is  transportation,  or  the 
change  in  place  of  wealth.  It  is  a  very  thin  line  which 
separates  this  class  from  the  preceding  class.  Transform- 
ing or  producing  wealth  consists  of  changing  the  position 
of  its  parts  relatively  to  each  other  ;  transporting  wealth 
is  changing  the  position  of  that  wealth  as  a  whole.  But 
"'part"  and  "whole"  are  themselves  loose  and  relative 
terms.  Bookbinding  is  a  transformation  or  production  of 
wealth;  it  assembles  the  paper,  leather,  thread,  and  paste 
into  a  whole  book.  Delivering  books  to  a  library  is  trans- 
portation. Yet  the  library  is,  in  a  sense,  a  whole;  and  to 
assemble  books  into  a  classified  and  organized  library  is  to 
make  a  whole  out  of  parts.  The  distinction  between  trans- 
formation and  transportation  is  thus  merely  one  of  conven- 
ience. Many  writers  prefer  to  include  them  both  under 
"production."  We  prefer  to  include  them  under  the  less 
ambiguous  and  more  inclusive  rubric  "interactions,"  and 
our  object  here  is  not  to  emphasize  their  difference,  but 


SEC.  5]  INCOME    SUMMATION  149 

their  similarity.  The  same  principle  of  equal  and  opposite 
services  applies  to  both.  When  merchandise  is  changed 
from  one  warehouse  to  another,  the  first  warehouse  is 
credited  with  the  change  and  the  second  debited.  The 
warehouse  which  has  rendered  up  the  merchandise  has 
done  a  service;  that  which  has  received  it  has  done  a 
disservice.  A  banker  who  takes  money  from  his  vault  and 
puts  it  in  his  till  will,  if  he  keeps  separate  accounts  for  the 
two,  credit  the  vault  and  debit  the  till.  When  wheat  is 
imported  from  Canada,  that  nation  is  credited  and  the 
Um'ted  States  is  debited  with  the  value  of  the  operation. 
We  may,  as  in  the  case  of  continuous  productive  pro- 
cesses, divide  up  transportation  districts  by  any  arbitrary 
lines,  and  consider  the  passage  of  any  articles  across  those 
lines  as  an  interaction. 

§5 

The  third  class  of  interactions  is  the  change  of  owner- 
ship of  wealth  or  property.  This  has  been  called  transfer. 
Transfers  usually  occur  in  pairs,  and  involve  two  objects 
transferred  in  opposite  directions  between  two  owners. 
This  double  transfer,  we  have  called  an  exchange.  Since 
an  exchange  consists  of  two  transfers,  and  since  a  transfer 
is  a  species  of  interaction  and  as  such  is  self-canceling, 
every  exchange  is  self-canceling  and  cannot  of  itself  con- 
tribute anything  to  the  total  income  of  society.1  When  a 
bookseller,  for  instance,  sells  a  book,  he  credits  his  stock 
with  the  fact  that  it  has  brought  in  money,  and  the  cus- 
tomer debits  his  library  to  the  same  amount. 

1  The  exchange  does  not  duplicate  income,  but  merely  shuffles  it 
about.  It  may  and  does  put  services  of  wealth  where  they  are  most 
needed,  and  thus  results  in  a  more  effective  use  of  income,  just  as 
credit  and  other  forms  of  the  divided  owner-hip  of  wealth  may  make 
a  more  effective  ownership  of  capital.  In  both  these  cases  there  is  an 
increase  of  "total  utility."  This  needs  to  be  considered  in  its  proper 
place,  but  it  must  not  stand  in  the  way  of  our  canceling  the  values 
of  assets  and  liabilities  or  of  services  and  disservices.  These  values, 
as  is  well  known,  are  connected,  not  with  total  utilities,  but  with  mar- 
ginal utilities. 


150  NATURE    OF   CAPITAL   AND   INCOME          [CHAP.  IX 

These  two  items  constitute  the  transfer  between  the 
stock  of  books  of  the  dealer  and  the  stock  of  books  of  the 
customer.  The  remaining  two  items  constitute  a  transfer 
between  the  stocks  of  cash  of  the  two  men;  the  dealer 
debits  his  "  cash  "  and  the  customer  credits  his. 

When  therefore  an  article  of  wealth  changes  hands, 
it  occasions  an  element  of  income  to  the  seller  and  an 
element  of  outgo  to  the  purchaser,  and  therefore  no  income 
at  all  to  society.  The  effect  of  canceling  these  items  — 
the  credit  item  of  the  seller  and  the  debit  item  of  the  pur- 
chaser —  is  to  free  the  income  account  of  that  article  from 
all  entanglements  with  exchange,  to  wipe  out  all  money 
income,  and  to  leave  exposed  to  view  what  we  have  called 
the  natural  income  of  the  article.  Thus,  books  yield  their 
natural  income,  not  when  the  book  dealer  sells  them,  but 
when  the  reader  peruses  them.  The  sale  is  a  mere  pre- 
paratory service,  a  credit  item  to  the  book  dealer  and  a 
debit  item  to  the  buyer.  The  fact  of  bookselling  adds 
nothing  to  the  income  of  society,  but  the  reading  of  the 
book  does.  Again,  a  forest  of  trees  yields  no  natural 
income,  until  the  trees  are  felled  and  pass  into  then  ext 
stage  of  logs.  The  owner  of  the  forest  may,  to  be  sure, 
"realize"  on  the  forest  long  before  it  is  ready  to  be  cut, 
by  simply  selling  it  to  another ;  and  to  him  the  forest  has 
then  yielded  income ;  but,  as  the  purchaser  has  suffered  an 
equal  outgo,  the  forest  has  as  yet  yielded  nothing  to  society. 

The  principle  that  an  article  of  capital  yields,  to  society, 
no  income  except  its  natural  income,  is  not  altered  when 
its  ownership  is  divided  nor  when  the  part  rights  are 
bought  and  sold.  Adam  Smith  regarded  a  rented  house 
as  bearing  income  in  the  form  of  rent,  but  a  house  occu- 
pied by  the  owner  as  bearing  no  income  at  all.  The  truth 
is  nearly  the  reverse.  Both  houses  yield  income,  and  both 
incomes  are  of  the  same  kind,  viz.  shelter.  The  rent  of  the 
rented  house  is,  for  society,  not  income  at  all.  It  is  income 
to  the  landlord  but  outgo  to  the  tenant,  —  outgo  which  he 


SEC.  5]  INCOME    SUMMATION  151 

Is  willing  to  suffer  solely  because  of  the  shelter  he  receives. 
This  shelter  alone  remains  as  the  income  from  the  house 
after  the  rent  transaction  is  canceled  out  between  the  two 
parties  concerned.  The  shelter-income  is  the  essential  and 
abiding  item,  and  without  it  there  could  be  no  rent-income 
to  the  landlord. 

Again,  a  railway  yields  as  its  income  solely  the  natural 
one  of  transporting  goods  and  passengers.  Its  owners  sell 
this  transportation  service  for  money  and  regard  the  rail- 
way simply  as  a  money  maker;  but  to  the  shippers  and 
passengers  this  same  money  is  an  expense  and  exactly  off- 
sets the  railway's  money  earnings.  Of  the  three  items  — 
money  income  of  the  road,  money  outgo  of  its  patrons, 
and  transportation  —  the  first  two  mutually  cancel  and 
leave  only  the  third,  transportation,  as  the  real  contribu- 
tion of  the  railway  to  the  sum  total  of  income. 

We  see,  then,  that  the  method  of  couples,  applied  to 
buyer  and  seller,  denudes  all  capital  of  its  so-called 
'' money-income,"  and  lays  bare  the  only  income  it  can 
really  produce,  the  natural  income.  We  see  that  capital 
is  not  a  money-making  machine,  but  that  its  income  to 
society  is  simply  its  services  of  production,  transporta- 
tion, and  gratification.  The  income  from  the  farm  is  the 
yielding  of  its  crops;  from  the  mine,  the  production  of  its 
ore;  from  the  factory,  its  transformation  of  raw  into  fin- 
ished products;  from  commercial  capital,  its  passage  of 
goods  from  producer  to  consumer;  from  articles  in  con- 
sumers' hands,  their  enjoyment  or  so-called  "  consumption." 

Similar  principles  apply  to  outgo,  no  part  of  which,  for 
society,  exists  in  money  form.  The  great  bulk  of  what  mer- 
chants call  "cost  of  production,"  expense,  or  outgo,  consists 
of  money  costs  which  carry  with  them  their  own  cancella- 
tion. For  manufacturers,  merchants,  and  other  business 
men,  almost  every  outgo  is  an  expense,  i.e.  consists  of  a 
money  payment.  Such  money  payments  are  for  wages, 
:'aw  materials,  rent,  and  interest  charges.  Now  all  these 


152  NATURE    OF   CAPITAL   AND    INCOME          [CHAP.  IX 

outgoes  are  incomes  for  other  people.  The  wages  are  the 
earnings  of  labor;  the  payment  for  raw  material  is  re- 
ceived by  some  other  manufacturer ;  the  rent  by  the  land- 
lord; the  interest  charges  by  the  creditor. 

Not  only  do  exchange  transactions  completely  cancel 
themselves  out  in  reckoning  total  income,  but  the  great 
majority  of  the  natural  services  of  capital  do  so  also. 
Even  these  natural  uses  of  capital  consist,  for  the 
most  part,  of  " interactions,"  -they  are  transformations 
or  transportations  of  wealth.  These  intermediate  stages 
are  merely  preparatory  to  the  final  use  or  so-called  "con- 
sumption" of  wealth,  and,  after  the  interactions  have  been 
canceled  out,  do  not  enter  as  items  either  on  the  income 
or  outgo  side  of  the  social  balance  sheet. 

In  order  to  showr  the  effect  of  canceling  out  the  equal 
and  opposite  items  entering  into  every  interaction 
throughout  the  productive  processes,  let  us  observe  the 
various  stages  of  production  which  begin  with  the  forest 
above  referred  to.  The  product  of  the  forest,  its  gross  in- 
come, is  the  series  of  events  called  the  turning  out  of  logs. 
This  log-production  is  a  mere  preparatory  service,  a  credit 
item  to  the  forest  and  a  debit  item  to  the  stock  of  logs  of 
the  saw  mill,  to  which  they  next  pass.  As  the  sawmill 
turns  its  logs  into  lumber,  the  lumber  yard  is  debited  with 
the  production  of  lumber,  and  the  sawmill  is  credited  with 
its  share  in  this  transformation. 

Intermediate  categories  may,  of  course,  be  created,  and 
we  may  follow,  in  like  manner,  the  further  transformation, 
transportation,  and  exchange  to  the  end  of  the  stages  of 
production,  or  rather,  to  the  ends;  for  these  stages  split  up 
and  form  several  streams  flowing  in  different  directions. 
To  indicate  merely  one  of  these  streams,  let  us  suppose  that 
the  lumber  which  goes  out  from  the  yard  is  used  in  repairing 
a  certain  warehouse.  The  warehouse  is  used  for  storing 


SEC.  6]  INCOME   SUMMATION  153 

cloth;  the  cloth  goes  from  the  warehouse  to  the  tailor; 
the  tailor  converts  the  cloth  into  suits  for  his  customers;  and 
his  customers  receive  and  wear  those  suits.  In  this  series,  all 
the  intermediate  services  cancel  out  in  "couples"  and  leave 
as  the  only  uncanceled  element,  or  final  fringe  of  services, 
the  use  of  clothes  in  consumers'  hands. 

Should  we  stop  our  accounts,  however,  at  earlier  points 
in  the  series,  the  uncanceled  fringe  will  be  not  consumers' 
services,  but  the  positive  side  of  intermediate  services  or 
interactions.  The  negative  side  will  not  appear,  as  it  be- 
longs to  later  stages  in  the  series.  This  will  all  be  clear,  if 
we  put  the  matter  in  figures,  stage  by  stage.  The  follow- 
ing are  the  items  for  the  logging  camp  above  mentioned, 
in  the  accounts  of  its  owner :  — 

INCOME  ACCOUNT  FOR  LOGGING  CAMP  FOR  YEAR  1900 

Income  Outgo 

Production  of  logs $50,000  (Omitted) 

The  gross  income  from  the  logging  camp,  considered  by 
itself,  and  without  any  deductions  for  expenses,  is  here  seen 
to  consist  in  the  production  of  $50,000  worth  of  logs.  If, 
however,  we  combine  the  logging  camp  with  the  sawmill,  we 
shall  have  accounts  like  the  following,  in  which,  to  avoid 
irrelevant  complications,  no  account  is  taken  of  any  ex- 
penses which  are  not  interactions  between  the  groups  of 
capital  considered :  - 

INCOME  ACCOUNT  FOR  LOGGING  CAMP  AND  SAWMILL  FOR  1900 


Capital  Source 

Income 

Outgo 

Logging  camp 
Sawmill 

Yielding  logs  to 
sawmill  .     .     .  $50,000 
Yielding  lumber 
to  lumber  yard  560,000 

Receiving    logs 
from  camp 

$50,000 

154  NATURE    OF    CAPITAL   AND    INCOME         [CiiAP.    IX 

In  this  case,  canceling  the  two  log  items  we  have  left  only 
the  lumber  item;  i.e.  the  income  from  the  combined  logging 
camp  and  sawmill  consists  only  of  the  production  of  lumber, 
its  final  product.  The  transfer  of  logs  from  one  department 
to  the  other  no  longer  appears.  This  transfer  is  like  the 
taking  of  money  from  one  pocket  and  putting  it  hi  another, 
as  is  particularly  evident  in  case  the  logging  camp  and 
sawmill  are  combined  under  the  same  management. 

Extending  the  same  principles  to  the  entire  series,  wTe  have 
the  accounts  as  given  on  the  opposite  page. 

It  should  be  noted  that  these  entries  relate  not  to  suc- 
cessive but  to  simultaneous  events ;  that  all  the  items  refer 
to  a  fixed  period  of  time ;  that  is  to  say,  we  are  not  following 
the  fortunes  of  the  original  logs  through  succeeding  stages, 
but  comparing  the  simultaneous  operations  of  the  series  of 
groups  of  instruments. 

If  we  successively  cancel  items  pair  by  pair  by  offset- 
ting any  item  on  the  right  side  by  the  item  in  the  line 
above  it  on  the  left  side,  we  shall  find,  if  we  stop  after  the 
first  two  cancellations,  that  the  net  income  from  logging 
camp,  sawmill,  and  lumber  yard,  consists  only  of  the  pro- 
duction of  retail  lumber,  $70,000 ;  it  does  not  include  either 
the  transfer  of  logs  or  the  transfer  of  wholesale  lumber.  In 
like  manner,  if  we  proceed  one  stage  further,  that  is,  if  we 
stop  our  cancellations,  at  the  end  of  the  first  four  interac- 
tions, the  production  of  retail  lumber  no  longer  appears  as 
an  element  of  income ;  and  so  on,  step  by  step  to  the  end, 
when  the  only  surviving  item  will  be  the  "wear"  of  the 
suits. 

It  is,  of  course,  true  that  in  any  actual  accounts  there 
will  be  numerous  other  items  than  those  which  have  been 
exhibited  in  this  simple  chainlike  fashion.  Were  it  worth 
while,  we  might  insert  these  additional  entries  of  income 
and  outgo  elements.  Most  of  them  would  consist  of  the  posi- 
tive or  negative  side  of  an  interaction,  and  if  we  were  to 
introduce  its  mate,  the  opposite  aspect  of  the  same  transac- 


SEC.  G] 


INCUMi:    SUMMATION 


155 


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156  NATURE    OF   CAPITAL   AND   INCOME          [CHAP.  IX 

tion,  it  would  be  necessary  to  include  still  other  accounts. 
If  we  should  follow  up  all  such  leads  we  should  soon  have  an 
intricate  network  of  related  accounts.  But  the  same  prin- 
ciple of  the  interaction  as  a  self-effacing  element  would  apply. 
The  only  items  of  outgo  which  are  not  the  negative  sides  of 
interactions  will  be  the  items  of  subjective  labor  and 
trouble.  These  alone  will  finally  remain  as  uncanceled 
elements  of  outgo. 

§7 

The  table  given  will  throw  light  on  the  question,  Of  what 
does  income  consist?  The  question  is  not  a  thoroughly 
definite  one.  If  we  ask  instead,  Of  what  does  the  income 
from  a  particular  group  of  capital  consist  ?  we  shall  make  it 
definite.  Whether  the  production  of  logs  is  income  or  not 
depends  upon  the  point  of  view.  It  is  income  from  the 
first  link  of  capital  (logging  camp)  in  our  series;  it  is  not 
income  from  the  first  two  links  combined,  for  in  the  second 
link  it  occurs  as  outgo.  Likewise,  the  use  of  the  ware- 
house is  true  income  with  respect  to  the  first  four  links 
or  groups  of  capital,  but  is  no  longer  income  when  the  fifth 
is  included. 

We  see,  therefore,  that  the  income  from  any  group  of 
capital  does  not  consist  in  any  degree  of  the  interactions 
taking  place  within  it,  but  only  of  the  final  or  outer  fringe 
of  services  performed  by  the  group.  As  the  group  is  en- 
larged, this  particular  outer  fringe  disappears  by  being 
joined  to  the  next  part  of  the  economic  fabric,  and  another 
fringe,  still  more  remote,  appears.  The  question  naturally 
arises,  When  is  the  economic  fabric  complete,  and  has  it  any 
final  outer  fringe  ?  But  this  question  must  be  deferred  for 
the  present. 

Nor  do  we  yet  inquire  what  relations  exist  between  the 
two  sides  of  the  same  account,  say  the  expense  to  the  saw- 
mill for  logs  and  its  income  from  sawn  lumber.  In  the  illus- 
trative tables  the  latter  is  entered  as  greater  than  the 


SEC.  8] 


INCOME    SUMMATION 


157 


former,  and  this  is  normally  the  case,  if  the  capital  of  the 
sawmill  remains  constant.  At  present,  however,  we  are 
not  concerned  with  the  effects  of  income  and  outgo  on 
capital,  but  only  with  the  summation  of  income. 


The  method  of  couples,  then,  is  useful  in  showing  of 
what  elements  income  consists  in  any  given  case.  The 
method  of  balances,  on  the  other  hand,  exhibits  the  amount 
of  income  contributed  from  each  article  of  capital  as  its 
source.  The  two  methods,  as  applied  to  the  example  just 
given,  are  as  follows :  — 


Capital 

Logging  camp 

Sawmill 

Lumber  yard 

Warehouse 

Stock  of  cloth  in  warehouse   . 
Stock  of  cloth  of  tailor 
Stock  of  clothes  of  customers 


METHOD  OF  BALANCES 

Income 


Outgo 


Net 
Incorn  e 


50,000-  .  .  .=+$50,000 
10,000 
10,000 
10,000 
10.000 
10,000 
10,000 


60,000  -  $50,000  =  + 

70,000  -  60,000  =  + 

80,000  -  70,000  =  + 

90,000-  80,000  =  + 

100,000-  90,000  =  + 

110,000-  100,000  =  + 


$110,000 


Outgo 


The  two  methods  —  balances  and  couples  —  show  the 
same  result,  but  from  different  points  of  view.  By  means 
of  the  method  of  balances  we  are  enabled  to  see  what  part 
of  the  final  net  income  is  contributed  by  each  of  the  articles 
in  the  group.  By  means  of  the  method  of  couples,  we  are 
enabled  to  see  of  what  the  net  income  from  the  entire  group 


158  NATURE   OF   CAPITAL   AXD   INCOME          [CHAP.  IX 

of  articles  consists;  canceling  by  the  oblique  lines,  we 
have  left  but  one  item,  $110,000,  representing  the  "  wear  " 
of  the  suits.  The  two  methods  must  not  be  confused. 
When  we  find  by  the  method  of  couples  that  the  net 
income  of  $110,000  consists  exclusively  of  the  use  of 
suits  of  clothes,  this  does  not  imply  that  this  net  income 
is  all  due  to  the  stock  of  clothes.  To  discover  to  what 
it  is  due,  recourse  must  be  had  to  the  method  of  balances. 
We  thereby  see  that  only  $10,000  of  it  is  due  to  the  stock 
of  clothes,  the  remainder  being  due  to  the  other  capital 
instruments  in  the  table  and  most  of  all  ($50,000)  to  the 
logging  camp.  Combining  the  results  of  both  methods, 
we  may  state  that  the  total  net  income  from  the  specified 
group  of  instruments  consists  of  $110,000  worth  of  "  wear  " 
of  suits  and  that  this  is  due  partly  to  the  stock  of  clothes 
and  partly  to  other  capital. 

The  two  methods,  that  of  balances  and  that  of  couples, 
correspond  in  a  general  way  to  the  two  methods  for 
canceling  liabilities  and  assets  in  capital  accounts.  The 
method  of  balances  gave,  it  will  be  remembered,  the 
amount  of  capital  belonging  to  each  individual ;  the  method 
of  couples  showed  of  what  elements  the  total  capital  con- 
sisted. 

§9 

We  have  now  followed  the  cancellations  to  which  inter- 
actions lead,  whether  they  be  interactions  of  exchange  or 
production.  The  case  of  exchange,  however,  needs  further 
consideration.  Since  every  exchange  consists  of  two  trans- 
fers, and  every  transfer  of  two  items,  a  credit  and  a  debit, 
the  exchange  evidently  consists  of  four  items  in  all,  two 
of  which  are  credits  and  two,  debits.  These  four  may  be 
paired  off  in  two  ways,  only  one  of  which  has  thus  far 
been  mentioned.  They  stand,  as  it  were,  at  the  four 
corners  of  a  square,  as  in  the  following  scheme,  which 
shows  the  credits  and  debits  involved  when  goods  worth  $2 


SEC.  9]  INCOME   SUMMATION  159 

are  sold.     The  dealer  credits  his  stock  of  goods  and  debits 
his  "cash,"  while  the  buyer  does  the  opposite. 


Stock  of  GowlK 

Stock  of  Cash 

Seller        

+  S2 

-$2 

Buyer       

-  S2 

-r$2 

The  two  transfers  into  which  any  exchange  may  be 
resolved  are  represented  by  the  two  columns  of  the  table. 
But  an  exchange  may  also  be  resolved  into  two  pairs  of 
items  represented  by  the  two  lines  of  the  table.  The 
items  in  the  same  horizontal  line  record  the  part  taken  in 
the  exchange  by  one  of  the  two  exchangers.  This  pair  of 
items  constitutes  his  transaction,  while  the  remaining  pair 
constitutes,  in  like  manner,  the  transaction  of  the  other 
party  to  the  exchange.  The  term  "  transaction,"  though 
somewhat  vague  in  ordinary  use,  appears  well  suited  to 
express  the  share  in  an  exchange  of  one  of  the  two  who 
participate  in  it. 

Every  exchange,  then,  consists  of  four  items,  and  may 
be  resolved  either  into  two  transfers  (one  for  each  prop- 
erty exchanged)  or  into  two  transactions  (one  for  each 
exchanger).  The  first  resolution  has  been  considered; 
we  proceed  now  to  the  second,  and  enter  the  subject  of 
"  double-entry  bookkeeping." 

By  double  entry  is  meant  the  record  of  every  double- 
faced  event  pertaining  to  a  particular  person,  whether  it 
be  a  transaction  of  that  person  with  another  or  an  in- 
teraction between  the  various  categories  of  capital  within 
his  own  possession.  Double-entry  book-keeping  is  most 
perfectly  illustrated  in  the  case  of  a  fictitious  person. 
The  following  account  represents  the  entries  during  a 
given  year  for  a  dry  goods  company.  In  this  account  we 
observe  that  every  item  on  the  income  side  is  balanced 


160 


NATURE   OF   CAPITAL   AND   INCOME          [CHAP.  IX 


by  an  equal  and  opposite  item  on  the  outgo  side.  All 
items  thus  paired  are  represented  by  the  same  letters,  the 
capitals  being  used  for  positive  items  and  the  small  letters 
for  negative. 


INCOME  AND  OUTGO  OF  DRY  GOODS  COMPANY,   FOR 
YEAR    1906 


Capital  Source 

Income 

Outgo 

Stock  of  Goods 

By  goods  sold.     $10,000  A 

To        goods 
bought      .   $5,000  c 
To  work   of 
selling       .     1,500ft 
To  storage   .     1  ,000  q 

Cash 

By  cash  taken  out 
for:  — 
rent   .     .     .      $1,2005 
purchases    .     .  5,000  C 
wages     .     .     .  1,600Z> 
interest     pay  - 
ment  ...      800  E 
profits  .     .     .  2.000F 

To   cash  re- 
c  e  i  v  e  d 
from  sales  $10,  000  a 

Store  Lease 

By  storage  service  $1,000  G 

To  rent  paid  $1,200  b 

Rights     to     and 
obligations 
from  employees 

By  clerk  work  .     $1,500# 

To  clerk  hire  $l,600d 

Bonded  debt 

To     interest 
paid      .     .       $800  e 

Capital  stock 

To        profits 
paid      .     .  $2,000  / 

Let  us  consider  the  first  item  of  capital,  the  stock  of 
goods.  This  yields  to  the  company  as  its  gross  income 
the  money  obtained  from  sales,  amounting  to  $10,000  (A). 
The  payment  of  this  money  into  the  cash  drawer  becomes  a 
debit  item  (a)  on  the  part  of  the  stock  of  cash.  Reversely, 
when  the  rent  is  paid  the  lease  of  the  store  is  debited  with 
SI 200  (6),  and  the  stock  of  cash  which  yields  this  value  of 


SEC.  0]  INCOME   SUMMATION  161 

income  is  credited  (/?).  In  like  manner  all  the  transactions 
involving  a  payment  or  receipt  of  cash  are  entered  on  one 
side  with  respect  to  the  cash,  and  on  the  opposite  side  with 
respect  to  some  other  capital  source.  The  category  of  the 
capital  source  called  "  rights  to  and  obligations  from 
employees  "  yields  a  certain  amount  of  clerical  work  and 
other  services  appraised  at  $1500.  This  item  credited  (//) 
to  the  above-named  source  is  here  debited  (h}  to  the  stock 
of  goods,  to  sell  which  requires  the  services  of  these 
employees.  It  may  be  that  it  should  be  debited  to 
the  store  which  they  clean,  or  to  some  other  article  of 
capital  on  which  they  do  work;  but  in  any  case  it  must 
be  debited  under  some  head  or  heads. 

It  will  be  seen  that  among  the  other  items  of  capital 
which  are  sources  of  income  or  outgo  are  the  bonds  and 
stocks  of  the  company.  The  bonds  absorb  $800  of  in- 
terest, and  the  capital-stock,  which  is  a  residual  claim  on 
the  company,  absorbs  any  surplus  of  cash  which  it  is 
decided  to  distribute  in  dividends. 

The  two  sides  of  the  account  of  such  a  fictitious  person 
necessarily  balance.  It  cannot  be  otherwise,  even  if  the 
company  accumulates  its  profit  instead  of  paying  it  to 
the  shareholders;  for,  as  has  been  seen,  the  money  thus 
received  is  debited  to  the  cash  account. 

In  practical  accounting,  the  items  would  usually  be  sim- 
plified somewhat.  It  would  not  ordinarily  be  worth  while 
to  make  an  appraisement  of  the  value  of  the  use  of  the  ware- 
house for  storage  as  distinct  from  the  storage  charge,  nor  of 
the  value  of  the  work  performed  by  the  employees  as  distinct 
from  the  wages  paid  them.  In  the  above  accounts  we  have 
purposely  distinguished  these  magnitudes,  estimating  the 
storage  benefit  as  S1000  though  the  rent  paid  for  it  is  S1200, 
and  estimating  the  work  done  by  employees  as  worth  $1500 
though  their  wages  were  $1600.  If.  instead,  we  estimate 
the  storage  benefit  at  the  rent  figure  and  the  employees' 
work  at  the  wages  figure,  our  accounts  would  contain  four 


162  NATURE    OF   CAPITAL   AND   INCOME          [CHAP.  IX 

items  of  $1200  and  four  of  $1600.  Of  these,  two  of  each 
might  well  be,  and  in  practice  usually  are,  dispensed  with. 
These  are  the  pair  of  items  "storage  service"  (G  and  g) 
and  the  pair  " clerk  work"  (H  and  h).  Omitting  these, 
which  are  both  appraised  items,  there  will  be  left  only 
cash  transactions.  These  may  be  further  simplified  by 
dispensing  with  the  two  categories  called  "store  lease" 
and  "rights  to  and  obligations  from  employees,"  by  placing 
the  rent  (6)  and  the  wages  (d)  under  the  head  of  "  stock  of 
goods."  In  other  words,  we  charge  the  expenses  for  rent 
and  wages  directly  against  the  goods  stored  and  cared  for 
instead  of,  as  in  the  table,  charging  against  them  "  storage 
service"  and  "work  of  selling."  There  is  no  difficulty  in 
recognizing  the  resulting  accounts  as  those  employed  in 
ordinary  bookkeeping.  Occasionally  the  more  elaborate 
accounting  is  necessary,  as  when  a  very  old  lease,  like  some 
still  in  force  in  London,  requires  only  a  nominal  rent  charge 
compared  with  the  benefits  conferred. 

§10 

In  the  case  of  real  persons,  however,  the  two  sides  do  not 
balance,  for  the  accounts  do  not  consist  solely  of  double 
entries.  To  show  this,  let  us  recur  to  the  accounts  of  the 
lawyer  considered  in  Chapter  VIII.  The  table  on  the 
opposite  page  reproduces  those  accounts,  with  some  of  the 
items  given  in  greater  detail. 

In  these  accounts,  as  in  the  previous  ones,  we  have  in- 
dicated the  like  items  on  opposite  sides  by  like  letters,  the 
positive  being  represented  by  capitals  and  the  negative 
by  small  letters.  We  observe  that,  as  in  the  corporation 
accounts,  many  of  the  items  will  "  pair."  But,  unlike  the 
corporation  accounts,  the  present  accounts  contain  a  resi- 
due of  items  which  will  not  pair.  The  letters  representing 
these  unpaired  items  are  designated  by  being  inclosed  in 
.square  brackets.  They  show  that  [B],  [C],  [D],  [0]  —  the 
shelter  of  the  house,  use  of  furniture,  use  of  food,  use  of 


SBC.  10] 


INCOME   SUMMATION 


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164  NATURE    OF   CAPITAL   AND   INCOME          [CiiAi>.  IX 

clothes,  jewelry,  etc.  —  constitute  a  kind  of  income  which 
does  not  appear  elsewhere  as  outgo. 

§11 

We  found,  when  studying  the  accounts  of  instruments,  the 
chain  of  productive  services  of  the  lumber  camp,  etc.,  that 
there  always  remains  some  outer  fringe  of  uncanceled  in- 
come produced  by  the  capitalistic  machine.  We  have  now 
reached  this  same  kind  of  outer  fringe  in  studying  the 
accounts  of  persons,  provided  they  are  real  persons.  This 
outer  fringe  consists  of  what  economists  have  usually  called 
"consumption."  All  other  services  are  merely  preparatory 
to  such  services,  and  pass  themselves  on  from  one  category 
of  capital  to  another.  Thus  the  income  from  investments, 
being  deposited  in  bank,  is  outgo  with  respect  to  the  bank 
account;  the  bank  account  yields  income  by  paying  for 
stocks  and  bonds,  food,  etc.,  but  in  each  case  the  same 
item  enters  as  outgo  with  respect  to  these  or  other  cate- 
gories of  capital.  In  all  these  cases  the  individual  receives 
no  income  which  is  not  at  the  same  time  outgo.  It  is 
only  as  he  consumes  the  food,  wears  the  clothes,  or  uses 
the  furniture  that  he  receives  income. 

The  question  still  remains  whether  the  fringe  we  have 
reached  is  the  final  outer  fringe,  or  whether  we  must  not 
proceed  one  step  further  and  regard  the  final  services  just 
mentioned  as  merely  interactions  between  a  man's  external 
wealth  and  his  own  body.  This  question  will  be  discussed 
in  the  following  chapter.  WTe  are  content  here  to  leave  the 
chains  of  services  at  the  point  where  they  reach  the  person 
of  the  recipient. 


CHAPTER  X 

PSYCHIC    INCOME 


THE  stage  at  which,  in  the  previous  chapter,  we  left  in- 
come may  be  called  the  stage  of  final  objective  services. 
In  other  words,  it  is  the  stage  at  which  the  wealth  of  the  ob- 
jective world  at  last  acts  upon  the  person  of  the  recipient  of 
income.  This  final  income  is  that  for  which  the  economist 
is  usually  in  search,  and  is  that  which  the  ordinary  statistics 
of  workingmen's  budgets  represent.  It  is  clear  from  what 
has  been  said,  that  in  this  final  net  income  all  interactions 
between  articles  of  external  wealth  drop  out,  —  all  the 
transformations  of  production,  such  as  the  operations  of 
mining,  agriculture,  and  industry,  all  the  operations  of 
transportation,  and  all  business  transactions  or  exchanges. 
For,  in  all  such  cases,  the  debits  and  credits  inevitably 
occur  in  pairs  of  equal  and  opposite  items.  The  only 
items  which  survive  are  the  final  personal  uses  of  wealth, 
ordinarily  called  "consumption."  Let  us  rather  call  them 
enjoyable  objective  services.  The  main  sorts  of  enjoyable 
objective  services  are  the  following :  services  of  nourish- 
ment, services  of  housing  and  warming,  services  of  clothing 
and  personal  adornment,  services  of  personal  attendance, 
services  of  amusement,  instruction,  and  recreation,  serv- 
ices of  gratification  of  vanity. 

§2 

It  is  usually  recognized  by  economists  that  we  must  not 
stop  at  the  stage  of  this  objective  income.1  There  is  one 
more  step  before  the  process  is  complete.  Indeed,  no 

1  See  Fetter's  Principles  of  Economics,  Xe\v  York,  1904,  Chap.  VI. 

165 


166  NATURE    OF   CAPITAL   AND   INCOME  [CHAP.  X 

objective  services  are  of  significance  to  man  except  as  they 
are  preparatory  to  subjective  satisfactions. 

The  final  subjective  services  come  through  the  human 
body.  No  agent  outside  the  body  can  yield  them.  All 
that  persons  or  things  outside  of  man  can  do  is  to  stimulate 
his  bodily  organism.  Even  what  are  called  services  of  amuse- 
ment or  instruction  cannot  directly  amuse  or  instruct  the 
mind;  they  can  only  affect  the  body.  An  instructive 
book,  for  instance,  renders  its  service  simply  and  solely  by 
reflecting  light  into  the  eye  of  the  reader.  It  is  necessary 
that  these  stimuli  on  the  optic  nerve  should  be  transmitted 
through  the  nervous  system  before  any  mental  instruction 
takes  place.  So  a  piano  can  of  itself  produce  no  sensations 
of  tone.  It  merely  produces  external  vibrations,  which, 
through  the  ear  and  auditory  nerve,  ultimately  result  in 
sensation.  All  sound,  sight,  taste,  smell,  touch,  come 
about  through  reactions  of  the  nervous  system  to  external 
stimuli.  A  man  who  receives  a  Turkish  bath  has  received 
enjoyable  income  in  the  objective  sense,  but  all  the  serv- 
ices of  the  water,  towels,  attendants,  and  other  cooperat- 
ing agencies,  while  credited  to  them,  must,  if  we  treat  man 
himself  as  capital,  be  regarded  as  debited  to  him.  They 
result  simply  in  cleaning  and  stimulating  his  skin.  They 
are  income  from  outside  agencies  absorbed  by  his  body  in 
order  that  he  may  later  experience  pleasant  sensations  or 
avoid  unpleasant  ones,  through  the  enjoyment  of  health. 
Similarly  the  use  of  clothing  and  shelter  prevents  the 
occurrence  of  the  sensation  of  cold,  but  their  immediate 
objective  service  is  simply  in  hindering  the  dissipation  of 
heat  from  the  body.  They  are  disservices  with  reference  to 
the  body,  just  as  similar  care  and  protection  of  a  horse  are 
disservices  with  reference  to  it. 

When  medicine  is  taken,  it  may,  from  the  objective  stand- 
point, be  counted  as  a  part  of  income,  just  as  food,  clothing, 
and  other  ordinary  items.  But  it  is  clear  that  the  services 
of  medicine  are  (or  are  supposed  to  be)  the  repairing  of  the 


SEC.  3]  PSYCHIC   INCOME  167 

body,  and,  although  credited  to  the  medicine,  should  be 
debited  to  the  body,  just  as  the  services  of  a  carpenter  are 
credited  to  him  but  debited  to  the  house  which  he  mends. 
So  the  services  of  a  dentist,  far  from  producing  any  immedi- 
ate satisfactions,  have  for  the  moment  quite  an  opposite 
effect,  but  result  later  in  better  service  of  one's  own  teeth. 
They  are  credited  to  the  dentist,  but  debited  to  the  body. 
The  "consumption,"  or  use  of  food,  though  it  is  a  service  of 
the  food,  is  a  disservice  of  the  body;  for  food  stands  in  the 
same  relation  to  the  body  as  fuel  to  a  furnace  or  repairs  to 
a  house.  The  final  income  consists  of  the  subjective  sat- 
isfaction of  appetite  and  the  other  satisfactions  which 
the  intake  of  food  enables  the  body  to  yield  to  the  mind. 
These  include  not  simply  the  immediate  gratification  of  the 
palate,  but  the  promotion  of  pleasant  sensations  or  the 
avoidance  of  unpleasant  ones  later  on.  In  other  words, 
the  consumption  of  food,  by  preserving  health  and  main- 
taining life,  enables  the  body  to  yield  better  and  longer- 
continued  income  to  the  mind  in  future  years,  just  as  the 
repairs  on  a  house  enable  it  to  yield  shelter  a  long  time  after 
the  repairs  are  made. 

§0 
3 

These  and  other  illustrations  will  show  that,  if  we  in- 
clude the  body  as  a  transforming  instrument,  while  we 
must  credit  with  their  respective  services  all  these  outside 
agencies,  such  as  food,  clothing,  dwelling,  furniture,  orna- 
ments, and  other  articles  which,  as  it  were,  bombard  a 
man's  sensory  system,  we  must  also  at  the  same  time  debit 
the  body  with  these  same  items.  In  this  case  the  only  sur- 
viving credit  items  after  these  equal  debits  and  credits  are 
canceled  are  the  resulting  final  satisfactions  in  the  human 
mind.  In  other  words,  in  order  that  the  external  world 
should  become  effective  to  man,  the  human  body  must  be 
considered  as  the  last  transforming  instrument.  Just  as 
there  is  a  gradual  transformation  of  services  through  the 


168  NATURE    OF    CAPITAL    AND    INCOME  [CHAP.  X 

farm,  flour  mill,  and  bakery,  so  is  there  a  final  transforma- 
tion within  the  human  body  itself.  It  is  a  sort  of  factory, 
the  products  of  which  are  the  only  final  uncancelecl  income 
of  the  consumer.  In  a  complete  view  of  productive  pro- 
cesses, the  human  machine  is  no  more  to  be  left  out  of  con- 
sideration than  machines  which  handle  the  wheat  in  its 
prior  stages. 

All  objective  income,  therefore,  is  entirely  erased  or 
negatived  as  soon  as  we  apply  our  accounting  to  the  body 
of  the  recipient.  The  services  of  which  that  income  consists 
empty  out,  as  it  were,  their  quota  into  the  human  body,  but 
the  ultimate  result  is  not  finally  received  until  it  emerges 
in  the  stream  of  consciousness. 

We  define  subjective  income,  then,  as  the  stream  of  con- 
sciousness of  any  human  being.  All  his  conscious  life, 
from  his  birth  to  his  death,  constitutes  his  subjective  in- 
come. Sensations,  thoughts,  feelings,  volitions,  and  all 
psychical  events,  in  fact,  are  a  part  of  this  income  stream. 
All  these  conscious  experiences  which  are  desirable  are  posi- 
tive items  of  income,  or  services;  all  which  are  undesirable 
are  negative  items,  or  disservices.  We  have  avoided  ex- 
pressly the  statement  that  subjective  income  consists  of 
pleasure,  or  of  pleasure  minus  pain.  These  terms  have  been 
too  loosely  used  by  economists,  and  such  use  has  involved 
them  in  unnecessary  controversy  with  psychologists.  It  is 
better  to  avoid  such  disputes,  and  content  ourselves  with 
the  simple  statement  that  subjective  events  which  are  de- 
sirable are  services,  and  those  which  are  undesirable  are 
disservices.  This  statement  conforms  to  the  definition  of 
services  and  disservices  originally  given,  and  does  not  com- 
mit us  to  any  psychological  theory  of  pleasure  or  pain. 
Some  psychologists  would  maintain  that  pain,  to  an  ascetic, 
may  be  just  as  much  an  object  of  desire  as  pleasure.1 

1  For  instance,  of  the  founder  of  the  Sacred  Heart  Order,  we  read 
that, — 

"Her  love  of  pain  and  suffering  was  insatiable.  .  .  .     'Nothing 


SEC.  4]  PSYCHIC   INCOME  169 

Nor  is  it  necessary  to  take  sides  in  the  controversies  re- 
garding the  relations  between  mind  and  body.  We  are 
not  concerned  with  cause  and  effect,  but  with  means  and 
end,  and,  whatever  may  be  the  causation  of  mental  states, 
the  human  body  is  certainly  the  means  by  which  the  good 
from  external  wealth  is  finally  communicated  to  the  con- 
sciousness of  the  owner. 

§4 

The  two  kinds  of  final  income,  the  physical  and  the 
psychical,  or  the  objective  and  subjective,  are  both  legiti- 
mate in  their  proper  spheres.  Usually  the  physical  and 
psychical  income  are  equal  to  each  other  in  value.  A  loaf 
of  bread  which  yields  ten  cents'  worth  of  services  presumably 
gives  ten  cents'  worth  of  immediate  satisfaction.  When  one 
enjoys  a  musical  concert  wrorth  one  dollar,  it  does  not  matter 
whether  we  say  that  the  services  of  the  musicians  in  pro- 
ducing vibrations  are  worth  one  dollar,  or  the  enjoyment 
which  these  vibrations  occasion  in  the  mind  is  worth  this 
sum.  When  rent  is  paid  for  a  house,  this  is  generally 
taken  to  measure  also  the  subjective  comfort  obtained 
through  it. 

Nevertheless,  there  are  several  points  at  which  the  valua- 
tions of  subjective  and  objective  income  are  different,  and 
three  of  these  are  sufficiently  important  to  emphasize. 

The  first  case  is  that  in  which  the  transformation  within 
the  body  takes  a  long  time.  Here  the  two  species  of  in- 
come do  not  correspond.  For  instance,  the  instruction 
received  by  an  apprentice  in  preparation  for  his  trade  is  a 
sen-ice  rendered  to  him  in  the  training  of  his  body  in  manual 
dexterity,  in  order  that,  a  few  years  later,  this  manual 
dexterity  may  increase  his  income-earning  power.  Ap- 

but  pain,'  she  continually  said  in  her  letters,  'makes  my  life  support- 
able.'" Bougand,  Hist,  dc  la  bienhcurcusc  Marguerite  Marie,  Paris, 
1894,  pp.  171,  265.  Cf.  also  pp.  3SG,  387.  Quoted  from  William 
James,  Varieties  of  Religious  Experience,  1902,  p.  310. 


170  NATURE    OF   CAPITAL   AND   INCOME  [CHAP.  X 

prenticeship  is,  as  it  were,  an  investment  in  the  body,  to  be 
returned  at  a  later  time  (with  interest),  just  as  the  plant- 
ing of  a  tree  is  an  investment  in  the  tree  in  order  that  its 
fruit  may  be  secured  in  later  years.  At  the  time  of  tree 
planting  there  is  no  net  income,  for  the  work  credited  the 
tree  planter  is  debited  the  tree;  it  is  only  when  in  after 
years  the  tree  bears  fruit  or  other  product  that  any  return 
is  obtained  from  the  planting.  Similarly,  the  work  of 
teaching  the  apprentice  should  be  credited  to  the  teacher 
and  debited  to  the  apprentice's  body;  the  final  satisfactions 
will  not  come  until  the  acquired  knowledge  becomes 
effective.  All  this  can  be  faithfully  recorded  only  in  the 
complete  accounting  which  includes  subjective  income. 

The  same  principles  apply  to  any  training  or  education 
for  a  profession.  When  a  young  man  studies  law,  medi- 
cine, journalism,  music,  or  prepares  for  any  other  profes- 
sion, he  is  investing  in  his  own  person,  with  the  hope  that 
the  sums  thus  invested  may  ultimately  be  returned  to  him 
(with  interest).  The  same  is  true  of  physical  training. 
Many  of  the  most  successful  men  are  those  who,  like 
President  Roosevelt,  in  early  life  saw  the  wisdom  of 
developing  a  strong  body,  and  in  consequence  have  in- 
creased their  productive  power  in  mature  years. 


The  second  point  at  which  subjective  and  objective 
income  diverges  is  found  in  occupations  whose  special  grati- 
fication or  irksorneness  renders  their  return  in  psychical  in- 
come widely  different  from  their  return  in  objective  income. 
This  is  frequent  in  conditions  of  labor.  Properly  speaking, 
objective  income  takes  no  account  of  the  toil  of  the  laborer. 
The  workingman  who  earns  S2  a  day  earns  double  the  ob- 
jective income  of  one  who  earns  SI  a  day.  Yet  if  the  work 
of  the  former  is  difficult,  loathsome,  or  dangerous,  it  may 
well  be  that  many  would  prefer  the  nominally  smaller  in- 
come rather  than  endure  these  disadvantages.  These  facts 


SEC.  5]  PSYCHIC   INCOME  171 

have  often  puzzled  economists,  and  the  question  has  been 
asked  whether  any  allowance  should  be  made  for  disagree- 
able trades,  such  as  that  of  the  hangman,  and  whether  it  is 
fair  to  say  that  a  workingman  who  earns  $500  a  year  by 
the  sweat  of  his  brow  really  gets  as  much  as  a  capitalist 
who  receives  an  effortless  $500  from  stocks  and  bonds. 
The  answer  to  these  questions  is  now  evident.  So  far  as 
objective  income  is  concerned,  no  allowance  should  be 
made.  That  is,  the  returns  to  the  laborer  are  all  to  be 
counted  gross  and  not  net,  no  deduction  being  made  on 
account  of  so-called  "mental  anguish"  or  painful  feelings. 
Objective  income  stops  at  the  threshold  of  the  laborer's 
body.  It  does  not  follow  beyond  this  point  and  include 
what  the  body  communicates  to  the  mind.1 

But,  by  passing  to  subjective  income,  we  avoid  some  of 
the  manifest  unfairness  in  the  usual  statistical  comparisons 
which  contrast  a  capitalist's  income  with  that  of  a  laborer, 
or  contrast  with  each  other  the  incomes  of  various  labor- 
ers, some  of  whose  tasks  are  difficult  and  others  easy.  To 
obtain  one's  net  income  wre  must  subtract  from  the  sub- 
jective satisfactions  the  subjective  efforts  of  attainment. 
A  laborer  who  receives  $2  a  day  may  work  so  hard  for  it 
as  to  justify  a  deduction  of  $1.50  for  the  effort,  whereas 
the  laborer  who  receives  $1  a  day  may  possibly  need  to 
deduct  only  25  cents.  The  nominally  $2  man  would  then 
be  receiving  a  net  income  of  only  50  cents  a  day,  whereas 
the  nominally  $1  man  would  be  receiving  one  worth  75 

1  The  only  way  in  which  a  man's  person  contributes  to  such  objec- 
tive income  is,  as  has  been  implied  in  our  illustrative  accounts,  through 
the  work  he  performs  upon  external  objects,  in  order  that  these  may,  in 
turn,  yield  back  service  to  him.  Objective  income  thus  includes  all 
the  results  of  his  own  bodily  exertions  so  far  as  they  come  to  him  via 
these  outside  agencies.  A  farmer,  for  instance,  sows  wheat,  which 
is  sold  and  yields  him  income.  The  farmer's  services  here  start  a 
circuitous  process  which  is  transmitted  through  the  farm,  the  crops, 
the  wheat,  the  proceeds  from  selling  the  wheat,  the  enjoyable  com- 
modities purchased  with  these  proceeds,  and  finally  his  own  person 
again,  to  which  those  commodities  minister. 


172  NATURE    OF   CAPITAL   AND   INCOME  [CHAP.  X 

cents.  Again,  in  the  comparison  between  the  capitalist's 
and  laborer's  income,  we  ought  to  say  that  the  laborer 
who  receives  S500  a  year,  with  an  expenditure  of  effort 
appraised  at  $250,  is  only  receiving  one  half  as  great  an 
income  as  the  capitalist  who  obtains,  during  the  same 
period,  dividends  and  interest  to  the  extent  of  $500,  with 
no  effort  whatever. 

It  may  be  asked  how  an  appraisement  of  labor  is  possible. 
From  a  practical  or  statistical  standpoint  the  appraisement 
is  difficult,  if  not  impossible.  Yet  certain  data  are  obtain- 
able. A  servant  applying  for  work  asks  not  simply  in 
regard  to  the  wages,  but  in  regard  to  the  difficulty  of  the 
work,  and  will  consent  to  do  extra  or  disagreeable  tasks  only 
on  condition  of  a  definite  increase  in  wages.  In  this  case 
we  may  say  that  the  increase  in  wages  which  is  necessary 
to  procure  the  consent  of  the  laborer  represents  subjectively, 
to  him  or  her,  the  increased  difficulty  of  the  work.  In  like 
manner,  a  government  employee  who  has  at  any  time  the 
option  of  retiring  on  half-pay  may,  at  the  point  when  he  de- 
cides to  retire,  be  said  to  regard  the  difficulty  of  his  work 
as  equal  in  his  estimation  to  half  of  the  income  he  receives 
for  it. 

In  general  we  may  say  that  the  proper  method  of  apprais- 
ing the  disagreeable  element  involved  in  one's  work  is  to  de- 
duct from  the  gross  income  that  sum  which  the  worker  would 
be  willing  to  sacrifice  were  it  possible  for  him  so  to  avoid  the 
disagreeable  element.  That  is,  he  is  supposed  to  imagine 
an  alternative  condition,  considered  as  an  equivalent  in  his 
mind  to  the  actual  conditions  under  which  he  works,  but 
which  differs  from  them  in  two  particulars :  in  being  free 
from  the  labor  or  pain  of  toil ;  and  being  deprived  of  a  cer- 
tain amount  of  its  earnings  or  rewards.  If,  for  instance, 
the  laborer  who  obtains  $2  a  day  for  eight  hours'  work 
estimates  that  this  would  be  to  him  the  equivalent  of  $1.50 
without  labor,  he  has  virtually  made  a  deduction  of  50 
cents  a  day  for  the  irksomeness  of  his  work. 


SEC.  G]  PSYCHIC   INCOME  173 

§6 

We  have  reached  a  convenient  place  in  which  to  empha- 
size a  point  of  great  importance,  but  one  which  is  seldom 
understood.  This  is,  that  most  of  what  is  called  "cost  of 
production"  is,  in  the  last  analysis,  not  cost  at  all.  We 
have  found,  in  using  the  method  of  couples,  that  every 
objective  item  of  cost  is  also  an  item  of  income,  and  that  in 
the  final  total,  no  objective  items  of  outgo  survive  cancellation. 
This  principle  holds  true  whether  we  stop  our  accounts  at 
the  bodily  threshold,  confining  them  to  a  record  of  ob- 
jective income,  or  extend  them  to  include  the  body,  thus 
yielding  a  record  of  psychic  income.  Those  who  have 
been  accustomed  to  construct  their  theories  of  political 
economy  on  the  assumption  that  "cost  of  production"  is 
an  essential  and  ultimate  item,  may  do  well  to  reflect  care- 
fully on  this  proposition.  It  means  that  in  a  comprehen- 
sive view  of  production  there  is  no  cost  of  production  in  its 
objective  sense  at  all.  All  of  what  is  ordinarily  called  cost 
is  really  cost  only  with  respect  to  certain  accounts;  it  is 
always  also  income  with  respect  to  other  accounts.  This 
is  true,  for  instance,  of  the  cost  of  raw  materials.  It  costs 
flour  to  produce  bread ;  but  all  that  the  flour  costs  to  the 
baker  is  income  to  the  miller.  The  same  is  true  of  wages. 
The  employer  counts  his  pay  roll  as  cost  of  production, 
but  the  laborer  counts  it  as  earnings. 

Glimpses  of  the  fact  that  all  objective  costs  are  always  also 
objective  income,  and  therefore  disappear  in  the  final  sum- 
mation, are  occasionally  found  in  the  books,  especially 
those  on  land  and  interest,  although  the  points  of  view  have 
been  variable  and  uncertain.  There  have  been  long  dis- 
cussions as  to  whether  rent  enters  into  cost  of  production. 
The  question  has  by  many  been  negatively  answered.1 
Bohm-Bawerk  has  also  maintained  that  interest  was  not 

1  See  the  interesting  remarks  of  Jevons  in  the  preface  to  his  Theory 
of  Political  Economy,  3d  ed.,  1888,  p.  xlvii. 


174 


NATURE   OF    CAPITAL   AND   INCOME  [CHAP.  X 


an  element  in  the  cost  of  production.  From  what  has 
been  said  it  is  evident  that  every  rent  and  interest  pay- 
ment, while  it  is  a  cost  to  the  payer,  is  income  to  the  payee. 
The  total  objective  income  of  society  consists  wholly  of 
positive  items,  such  as  the  use  of  food  and  furniture,  the 
shelter  from  houses,  and  the  other  direct  services  of  wealth. 
There  are  no  negative  items  in  the  account  of  social  income 
which  survive  in  the  form  of  "costs  of  production." 

When  we  turn,  however,  to  subjective  income,  we  find  the 
case  somewhat  different.  Including  the  human  organism 
as  capital  acted  upon  by  the  outer  world  and  itself  acting 
upon  the  inner  world  of  consciousness,  we  not  only  carry 
the  uncanceled  fringe  of  services  one  step  further  and 
obtain  as  net  income  the  subjective  satisfactions  from  the 
use  of  food,  clothing,  furniture,  dwelling,  etc.,  but  we  find  it 
necessary  to  include  also  the  subjective  efforts  put  forth  by 
human  beings  in  order  that  these  satisfactions  may  accrue. 

Thus,  to  revert  to  the  income  account  of  the  lawyer.  We 
found  that  his  net  income  consisted  of  the  use  of  house  $100, 
use  of  furniture  $50,  use  of  food  $150,  and  other  uses  $2500, 
making  a  total  of  $2800.  But  if  we  include  the  lawyer's 
own  person  in  our  accounts,  we  should  have  to  enter,  in 
addition  to  all  the  previous  items  of  income,  the 
following :  — 


Capital 
Source 


Self  •( 


Income 

Satisfactions     from 

shelter  .  .  .  .  100  [P] 
Satisfactions  from 

use  of  furniture  50  [Q] 
Satisfactions  from 

use  of  food  .  .150  [/?] 
Satisfactions  from 

other  uses       .     .  2500  [S] 


Outgo 


Shelter 


Use  of  furniture 


Consumption 
food  .     .     . 
Other  uses 
Labor  sacrifice 


of 


1006 


50  c 


150  d 

2500  o 
500  [t] 


Some  of  these  additional  items  are  subjective  and  some 
objective;  the  former  are  distinguished  by  italics.  It  is 
evident  that  the  objective  items,  here  debited  to  the  person 


SEC.  7]  PSYCHIC   INCOME  175 

of  the  recipient,  have  all  equal  and  opposite  counterparts 
in  the  accounts  as  given  in  Chapter  IX,  §10.  These 
same  items  were  there  entered  as  credits  and  constituted 
the  "  uncanceled  fringe"  of  final  objective  income.  They 
were  designated  as  [B],  [C],  [/)],  [0].  Now,  however, 
after  the  introduction  of  the  new  items,  they  cancel  with 
the  debits  of  like  letters,  b,  c,d,  o;  but  another  uncanceled 
fringe  appears,  namely,  [P],  [Q],  [R],  [S],  which  items  are 
wholly  subjective.  These  we  have,  for  convenience,  entered 
at  the  same  figures  as  their  objective  prototypes.  Their 
sum  is  therefore  also  $2800.  But  there  also  appears  a  sub- 
jective labor  cost,  [t],  of  $500  to  express  the  personal  labor 
and  pain  of  the  lawyer  in  his  work.  The  result  is  that 
his  net  subjective  income  is  not  equal  to  the  objective  in- 
come of  $2800,  but  is  only  $2300. 

When  we  have  reached  this  final  stage  in  our  inquiries, 
therefore,  we  find  the  only  ultimate  item  of  cost  to  be  labor 
cost,  or,  if  the  term  "labor"  be  not  itself  sufficiently 
broad,  labor,  anxiety,  trouble,  annoyance,  and  all  the  other 
subjective  experiences  of  an  undesirable  nature  which  are 
necessary  in  order  that  the  experiences  of  an  agreeable  na- 
ture may  be  secured.1  In  a  sense,  therefore,  the  socialists 
are  quite  right  when  they  say  that  labor  is  the  only  true  cost 
of  production,  although  some  of  the  conclusions  which  they 
deduce  from  this  proposition  are  not  justifiable. 


The  third  discrepancy  between  subjective  and  objective 
income  is  due  to  the  fact  that  certain  agreeable  and  dis- 
agreeable experiences  are  due  directly  to  the  character  of 

1  It  may  be  well  here  to  emphasize  the  distinction  between  work 
and  labor  which  has  been  so  well  drawn  by  Professor  J.  B.  Clark. 
The  work  performed  consists  of  the  services  rendered,  and  is  posi- 
tive; the  labor  consists  of  the  efforts  of  performing  those  services 
and  is  negative.  The  work  is  objective;  the  labor  is  subjective. 
Properly  speaking,  an  employer  does  not  pay  a  man  for  his  labor, 
but  for  his  work. 


176  NATURE   OF   CAPITAL   AND   INCOME  [CHAP.  X 

the  body  itself.  A  large  part  of  our  subjective  income  is 
due  to  our  condition  of  health  or  disease.  A  man  with  a 
good  constitution  has  a  more  agreeable  stream  of  con- 
sciousness, or  subjective  income,  than  one  without.  The 
pains  and  sufferings  of  illness  here  find  a  place  in  the  com- 
plete accounts  of  income  and  outgo.  It  is  evident  that 
the  wealthy  man  who  confessed  that  he  would  exchange  all 
his  millions  for  a  young  and  vigorous  body  may  be  the 
recipient  of  a  large  objective  income,  but  not  enjoy  as 
much  subjective  income  as  Walt  Whitman,  who  had 
scarcely  a  dollar  in  the  world. 

That  these  subjective  items  are  by  no  means  to  be  de- 
spised by  the  economist,  who  has  far  too  long  busied  himself 
with  a  study  of  the  superficial  objective  phenomena,  is  evi- 
dent when  we  consider  that  a  healthy  body  is  absolutely 
essential  for  receiving  and  enjoying  the  income  from  external 
wealth.  The  man  who  is  short-sighted  enough  to  lose  his 
health  in  the  pursuit  of  what  he  calls  wealth  will  soon  be 
spending  all  of  this  sort  of  wealth  to  regain  health ;  and  we 
need  only  visit  the  health  resorts  of  Colorado  and  California 
to  be  struck  with  the  number  of  cases  of  business  men  who 
have  found  themselves  in  this  predicament.  Economists, 
by  fixing  attention  exclusively  on  physical  phenomena, 
leave  out  of  account  the  most  essential  element  of  all,  the 
vigor  of  human  life.  The  true  "wealth  of  nations"  is  the 
health  of  its  individuals.  A  nation  consisting  of  weak, 
sickly,  and  short-lived  individuals  is  poor  compared  with  a 
nation  whose  inhabitants  are  of  the  opposite  type.  Hence 
it  is  that  the  devices  of  modern  hygiene,  sanitation,  and 
preventive  medicine,  which  tend  to  increase  human  work- 
ing power  and  enjoying  power,  are  of  greater  economic 
import  than  many  of  the  luxurious  and  enervating  devices 
commonly  connoted  by  "  wealth." 

We  see,  then,  that  subjective  income  means  simply  one's 
whole  conscious  life.  Every  item  of  it  comes  via  the  body 
of  the  person. 


SEC.  8]  PSYCHIC   INCOME  177 

§8 

As  to  the  measurement  of  the  items  entering  into  this 
psychic  stream,  the  same  principles  apply  which  have 
already  been  laid  down  for  the  measurement  of  other  mag- 
nitudes. First,  all  like  events  are  measured  by  simple 
counting.  Secondly,  so  far  as  it  is  possible,  a  valuation  in 
terms  of  money  is  placed  on  them,  as  on  objective  services. 
To  accomplish  this  appraisement  it  is  only  necessary  for  the 
individual  to  answer  the  question  what  money  is  he  willing 
to  pay  for  any  enjoyment  brought  about  by  means  of  exter- 
nal wealth,  such  as  a  box  of  sweets  or  a  cigar.  If  the  event 
is  one  which  cannot  be  connected  with  purchasable  com- 
modities, it  is  necessary  to  imagine  an  exchange,  even  when 
actual  exchange  is  impossible. 

We  have  now  followed  the  method  of  couples  from  the 
balance  sheet  for  a  particular  article  of  capital,  or  group 
of  articles,  to  the  entire  capital  goods  of  an  individual  or 
of  society.  The  result  has  been  inevitably  to  lead  us  to  a 
consideration  of  the  psychic  stream  of  events  as  final  in- 
come, all  the  agreeable  items  being  on  the  credit  side  and 
the  disagreeable  ones  on  the  debit  side.  But  the  methods 
which  have  been  given  also  enable  us  to  stop  at  any  earlier 
point.  There  are  two  such  earlier  points  which  are 
convenient  and  logical.  The  final  objective  income  is  one; 
the  other  has  its  existence  only  in  a  highly  developed 
civilization  like  the  one  now  existing  in  western  Europe 
and  America,  and  consists  of  the  familiar  "money  in- 
come" of  an  individual,  that  is,  his  money  receipts  from 
all  capital  sources,  less  his  money  outgo  to  them.  The 
income  of  a  person  reckoned  by  these  three  methods  will 
ordinarily  be  very  similar,  though  in  theory,  and  sometimes 
in  practice,  it  may  differ  widely.  As  long  as  we  under- 
stand the  various  kinds  of  income,  and  the  relations  be- 
tween them,  we  are  at  liberty  to  consider  any  one  of  them 
as  "income"  in  its  proper  place.  But  we  can  scarcely 


178  NATURE    OF    CAPITAL    AND    INCOME  [CHAP.  X 

understand  any  one  without  having  had  at  least  some 
view  of  both  of  the  others. 

§  9 

Having  completed  our  survey  of  the  summation  of  the 
elements  of  income,  we  may  properly  pause  to  classify  these 
items.  They  fall  naturally  into  three  groups.  The  first 
group  includes  those  items  of  income  which  are  positive 
and  not  negative,  that  is,  the  agreeable  experiences  of  sub- 
jective income,  for  these,  as  we  have  seen,  are  the  only 
final  uncanceled  positive  items.  The  second  group  in- 
cludes items  which  are  negative  but  not  positive,  namely, 
disagreeable  psychical  experiences,  and  consists  of  two 
classes:  (1)  the  labor  and  trouble  which  are  sacrificed  for 
the  sake  of  procuring  income  through  objective  channels, 
in  other  words,  the  toil  of  the  producer;  and  (2)  the  dis- 
agreeable impressions  produced  in  one's  consciousness  by  an 
abnormal  state  of  the  body,  as  aches,  pains,  and  all  sorts 
of  illness,  but  which  are  not,  like  toil,  voluntarily  incurred 
for  the  sake  of  future  return.  The  third  group  includes 
what  we  have  called  interactions,  or  items  which  are  at 
once  positive  and  negative,  according  to  the  point  of  view. 
Both  of  the  first  two  groups  are  entirely  subjective,  and 
the  last  is  entirely  objective.  The  third  group,  interac- 
tions, constitutes  by  far  the  bulk  of  the  items  entering 
into  income  accounts,  and  includes  all  of  those  which 
enter  into  practical  bookkeeping.  It  may  be  subdivided 
into  two  groups:  (1)  interactions  outside  of  the  human 
body,  and  (2)  interactions  between  external  wealth  and 
the  human  body,  or  what  have  been  called  "final  objec- 
tive services."  The  following  scheme  shows  further  sub- 
divisions :  — 


SEC.  0] 


PSYCHIC    INCOME 


179 


Services 


Pure  services  (subjective) 
Pure  disservices  (subjective) 


f  labor  (cost  of  production) 
[  pains  and  other  discomforts 


Interactions 


between  objective  wealth 

and  body  of  owner 
(final  objective  services) 


nutrition 

clothing 

housing 

amusements 

instruction 

etc. 


between 


f  agricultural 
f  production    {  manufacturing 

transportation 


objective . 
articles 


commerce 


.  etc. 


'  advertising 
organizing 
indemnifying 
etc. 


PART   III.    CAPITAL  AND  INCOME 

CHAPTER      XI.  FOUR  INCOME-CAPITAL  RATIOS 

CHAPTER    XII.  CONCEPT  OF  RATE  OF  INTEREST 

CHAPTER  XIII.  VALUE  OF  CAPITAL 

CHAPTER  XIV.  EARNINGS  AND  INCOME 

CHAPTER     XV.  INCOME  AND  CAPITAL  ACCOUNTS 

CHAPTER  XVI.  THE  RISK  ELEMENT 


CHAPTER   XI 

FOUR   INCOME-CAPITAL   RATIOS 
§1 

WE  have  now  learned  what  capital  and  income  are  and 
how  each  is  measured.  We  have  seen  that  capital  is  not  to 
be  confined  to  any  particular  part  or  kind  of  wealth,  but  that 
it  applies  to  any  or  all  wealth  existing  at  an  instant  of  time, 
or  to  property-rights  in  that  wealth,  or  to  the  values  of  that 
wealth  or  of  those  property-rights.  We  have  seen  that  in- 
come is  not  restricted  to  money  income,  nor  does  it  consist 
of  a  flow  of  commodities,  nor  is  it  a  composite  of  commodities 
and  services,  nor  is  it  necessarily  regular  in  its  receipt,  nor 
must  it  necessarily  be  such  as  to  leave  capital  unimpaired ; 
but  that  it  consists  simply  of  the  services  of  wealth,  and 
that,  analogously  to  capital,  income  may  be  measured 
either  by  the  mere  quantity  of  the  various  services  rendered, 
or  by  their  value.  We  have  seen  that  in  the  summation 
both  of  capital-value  and  of  income-value  there  are  two 
methods  available  for  canceling  positive  and  negative 
items  called  the  "method  of  balances"  and  the  "method 
of  couples."  By  the  method  of  balances  the  negative  items 
in  any  individual  account  are  deducted  from  the  positive 
items  in  the  same  account,  and  the  difference,  or  balance, 
shows  the  net  capital  (or  income,  as  the  case  may  be)  with 
which  that  account  deals,  whether  this  be  the  net  capital 
(or  income)  of  a  particular  owner,  or  of  a  particular  article 
or  group  of  articles  of  capital.  The  method  of  couples,  on 
the  other  hand,  cancels  items  in  pairs  and  is  founded 
on  the  fact  that,  as  to  capital,  every  liability  rela- 

183 


184  NATURE    OF   CAPITAL   AND   INCOME          [CHAP.  XI 

tion  has  a  credit  as  well  as  a  debit  side,  and  that,  as  to 
income,  every  interaction  is  at  once  a  service  and  a  dis- 
service. 

We  observed  that  the  method  of  couples,  fully  carried  out, 
reveals  respectively  wherein  capital  and  income  ulti- 
mately consist.  We  have  seen  that  such  a  summation, 
applied  to  capital,  gradually  obliterates  all  partial  rights, 
such  as  stocks  and  bonds,  and  leaves  as  the  final  result  the 
concrete  capital  wealth  of  a  community;  and  that  when 
the  method  of  couples  is  applied  to  income  accounts,  the 
"interactions"  involved  disappear,  leaving  an  uncanceled 
outer  fringe  of  services  and  disservices.  If  the  method  is 
continued  as  far  as  possible  in  the  world  of  objective  serv- 
ices, it  leaves  simply  the  direct  or  final  services  of  objec- 
tive wealth  as  they  affect  the  human  organism;  while, 
if  the  method  is  pushed  one  step  further,  it  leaves,  as  the 
final  income  stream,  simply  the  pleasant  and  unpleasant 
experiences  of  human  consciousness.  We  found  as  one 
result  of  our  study  that  so-called  cost  of  production  has  no 
existence  as  an  element  of  the  objective  income  stream,  and 
that,  therefore,  the  only  costs  of  production  which  are  not 
also  elements  of  income  are  the  subjective  labor  and  trouble 
of  those  engaged  in  that  production. 

We  have  seen  that  capital  and  income  are  in  many  re- 
spects analogous,  and  are  strictly  correlative ;  that  all  capi- 
tal yields  income  and  that  all  income  flows  from  capital  —  at 
least  when  the  term  "  capital  "  is  used  in  its  broader  sense, 
which  includes  human  beings.  The  old  proposition  of  the 
economists,  therefore,  that  capital  is  that  wealth  which 
yields  income,  is  correct,  although  the  idea  that  such  a 
statement  is  restrictive,  and  applicable  only  to  certain  kinds 
of  wealth,  is  incorrect. 

§2 

Since  capital  and  income  are  so  intimately  related,  it- 
becomes  necessary  to  examine  in  detail  what  their  relations 
are.  The  chief  relations  between  capital  and  income  are 


SEC.  2]  FOUR   INCOME-CAPITAL  RATIOS  185 

represented  by  four  ratios.  As  we  have  seen,  both  capital 
and  income  may  be  measured  either  in  quantity  or  value. 
It  follows  that  the  relation  of  income  to  the  capital  which 
bears  it  takes  four  different  forms,  according  as  the  income 
and  the  capital  are  measured  in  one  or  the  other  of  these 
two  ways.  These  four  forms  of  the  income-to-capital 
ratio  follow :  — 

(1)  The  ratio  of  the  quantity  of  services  per  unit  of  time 
to  the  quantity  of  capital  which  yields  those  services  may 
be  called  the  physical  productivity  of  capital.     Thus,  if  10 
acres  of  land  yield,  in  a  certain  year;  60  bushels  of  wheat,  the 
ratio  of  income  to  the  capital  may  be  expressed  as  6  bushels 
per  acre  per  year.     This  is  its  physical  productivity.     In 
like  manner,  if  10  looms  will  weave  500  yards  of  cloth  in  a 
day,  the  ratio  of  services  to  the  quantity  of  capital,  or  the 
physical    productivity    of    the    looms,    is    50    yards    per 
machine  per  day. 

(2)  The  ratio  of  the  value  of  the  income  from  capital  to 
the  quantity  of  the  capital  may  be  called  the  value  produc- 
tivity.    Thus,  if  10  acres  of  land  yield  a  net  return  worth 
$200  a  year,  the  value  productivity  is  $20  per  acre  per 
year.     This  is  what  has  ordinarily  been  called  the  rent  of 
land.     The  same  principles  apply  to  the  rent  of  a  dwelling 
or  of    any  other  article  of  capital.     Another  example  of 
value  productivity  is  found  in  the  wages  of  the  laborer. 

(3)  The  ratio  of   the  quantity  of  services  rendered  by 
capital  to  the  value  of  the  capital  may  be  called  its  phys- 
ical return.     Thus,  if  $100  worth  of  capital  applied  to  land 
in  the  form,  say,  of  agricultural  implements  adds  to  the  yield 
of  the  land  one  bushel,  the  physical  return  of  this  capital  is 
3-5-5-  of  a  bushel  per  year  per  dollar  invested.     Such  a  con- 
cept of  physical  return  is  familiar  to  students  of  classical 
economics  under  the  head  of  " doses"  of  capital  applied  to 
land. 

(4)  The  ratio  of  the  value  of  services  to  the  value  of  the 
capital  yielding  them  may  be  called  the  value  return.      Thus, 


186  NATURE    OF   CAPITAL   AND   INCOME          [CiiAP.  XI 

if  a  house  worth  $10,000  yields  in  any  given  year  a  net  rent 
of  $1000,  the  value  return  is  ten  per  cent  per  year.    An 
important  case  of  value  return  is  evidently  the  rate  of  in- 
terest. 
Thus  we  have  four  ratios :  - 

L  Quantity  of  services  per  unit  of  time.=  physical  productivity. 

quantity  of  capital, 
2-   Value  of  services  per  unit  of  time,       =  yalue  productivity. 

quantity  of  capital, 

3.  Quantity  of  services  per  unit  of  time,  =  phygical  retum 

value  of  capital, 

4.  Value  of  services  per  unit  of  time,      _  yalue  return 

value  of  capital, 

These  four  magnitudes  must  be  carefully  distinguished. 
They  are,  as  mathematicians  say,  of  different  "  dimensions." l 
This  fact  is  suggested  in  the  four  following  phrases,  which 
may  be  taken  as  typical :  - 

1.  Bushels  per  acre  per  year. 

2.  Dollars  per  acre  per  year. 

3.  Bushels  per  dollarjper  year. 

4.  Dollars  per  dollar  per  year. 

§0 
3 

The  failure  to  keep  these  four  magnitudes  clearly  dis- 
tinguished has  already  led  to  a  great  many  confusions  in 
economic  science.  The  spurious  distinction  between  rent  as 
the  income  from  "land"  and  interest  as  the  income  from 
" capital"  is  a  case  in  point.2  From  this  confusion  comes 
the  notion  that  land  differs  from  "capital"  in  that  there  is 
a  margin  of  cultivation  for  the  former  and  none  for  the 

1  For  a  mathematical  statement,  see  Appendix  to  Chap.  XI. 

2  The  error  is  fully  exposed  in  Cannan's  "What  is  Capital?"  Eco- 
nomic Journal,  June,  1897,  pp.  283-284,  and  in  Fetter's  "The  Rela- 
tions between   Rent  and   Interest,"   a   paper  presented  before  the 
American  Economic  Association,  December,  1903.     See  also  Hicks's 
Lectures  on   Economics,   Cincinnati,   1901,  p.   228,  and  the   present 
writer's  "  R61e  of  Capital  in  Economic  Theory,"  Economic  Journal, 
December,  1897,   p.    524,    and   "Precedents   for  Denning   Capital," 
Quarterly  Journal  of  Economics,  May,  1904. 


SEC.  3]  FOUR    INCOME-CAPITAL    RATIOS  187 

latter;  and  that,  whereas  different  qualities  of  land  bear 
different  rents,  representing  the  difference  in  advantage 
between  a  particular  grade  of  land  and  no-rent  land,  all 
parts  of  capital  bear  the  same  rate  of  interest.  These 
errors  come  from  unconsciously  regarding  the  land  in 
terms  of  quantity  and  the  so-called  "capital"  in  terms  of 
value;  in  other  words,  from  considering  the  income  from 
land  in  the  sense  of  value  productivity,  but  that  from  capi- 
tal in  the  very  different  sense  of  value  return.  If,  in  mak- 
ing our  comparisons,  we  abide  consistently  by  either  one 
of  these  ratios,  the  imagined  distinction  between  rent  and 
interest  and  between  land  and  capital  will  vanish.  It  is 
quite  true  that  the  value  productivity  of  land  differs  with 
different  grades  of  land;  but  it  is  equally  true  that  the 
value  productivity  of  machinery,  or  of  any  other  element  of 
capital,  so  varies.  New,  high-grade,  and  efficient  machinery 
bears  exactly  the  same  relation  to  machinery  which  is  out 
of  date  and  inefficient  that  fertile  land  bears  to  sterile. 
Similarly,  different  persons  have  different  degrees  of  pro- 
ductivity, some  having  high  and  others  low  earning  power. 
It  was  on  this  basis,  in  fact,  that  Francis  Walker  applied 
the  Ricardian  theory  of  rent  to  the  explanation  of  entre- 
preneur's profits. 

On  the  other  hand,  if  we  fix  our  attention  on  value  return, 
we  find  it  indeed  true  that  the  value  return  called  the  rate  of 
interest  on  " capital"  (however  narrowly  capital  may  be 
conceived)  is  uniform,  but  we  find  it  equally  true  that  the 
value  return  on  land  is  also  uniform ;  for  land  which  yields 
a  high  rent  will  have  a  correspondingly  high  value,  and,  in 
consequence,  the  ratio  of  the  rental  to  the  value  will  be 
exactly  the  same  as  for  lower  grades. 

Other  examples  of  confusion  might  be  cited.  We  find 
some  of  them  in  the  cruder  theories  of  interest.  The 
"naive"  productivity  theory,1  for  instance,  confuses  phys- 

1  See  Bohm-Bawerk,  Capital  and  Interest,  English  translation,  1888, 
pp.  120-141. 


188  NATURE    OF   CAPITAL   AND    INCOME          [CHAP.  XI 

ical  productivity  and  value  return,  and  attempts  to  deduce 
the  rate  of  interest  from  mere  physical  productivity,  which 
is  impossible. 

§4 

In  this  book  we  are  concerned  chiefly  with  the  fourth 
relation,  value  return,  or  the  ratio  of  the  value  of  income 
to  the  value  of  capital. 

The  fundamental  principle  which  applies  here  is  that  the 
value  of  capital  at  any  instant  is  derived  from  the  value  of 
the  future  income  which  that  capital  is  expected  to  yield. 
The  expected  services  may,  of  course,  not  be  the  actual 
services.  In  our  ignorance  of  the  future  we  fix  our  present 
valuations  on  the  basis  of  what  we  expect  the  future  to  be. 

The  principle  of  present  worth  is  of  fundamental  impor- 
tance in  the  theory  of  value  and  prices.  It  means  that  the 
value  of  any  article  of  wealth  or  property  is  dependent  alone 
on  the  future,  not  the  past.  The  principle  has  been  imper- 
fectly stated  as  follows:  "The  value  of  any  article  is  not 
determined  by  its  cost  of  production,  but  by  its  uses." 
But  the  costs  of  production  are  disservices,  and  these,  if  they 
be  future,  enter  into  value  on  precisely  the  same  terms  as 
uses  or  services.  They  are  discounted  as  are  services. 
For  instance,  the  value  of  the  Panama  Canal  to-day  is 
dependent  upon  the  future  expected  services,  taken  in  con- 
nection with  the  expected  cost  of  completion.  If  these 
future  elements  be  given,  the  value  of  the  canal  will  be  the 
same  whether  past  cost  was  large  or  small,  or  nothing  at 
all.  Of  course,  the  future  expected  cost  for  completing  the 
canal  is  less  than  if  some  of  the  work  had  not  been  done 
already,  so  that  the  greater  the  past  cost  has  been,  the  less 
the  future  cost  will  be,  and  hence  the  greater  the  value  of 
the  canal  at  present. 

Thus  normally  the  value  of  capital  will  vary  with  the 
past  cost  of  production.  Moreover,  the  experience  of  the 
past  enables  us  to  make  a  better  estimate  as  to  future  cost. 


SEC.  4]  FOUR    INCOMI-X'APITAL   RATIOS  180 

But,  however  determined,  it  is  the  estimated  future  cost 
alone  which  enters  into  the  calculation  of  present  value. 
All  of  these  principles  are  well  illustrated  in  the  case  of 
the  canal.  After  some  $300,000,000  had  been  sunk  in  the 
enterprise,  the  proprietors  were  willing  to  sell  out  for  only 
$40,000,000.  To  them,  therefore,  it  was  worth  less  than  it 
had  cost.  The  effect  of  the  work  already  done  on  the  canal 
was  certainly  to  lessen  the  labors  of  the  present  possessors, 
but  it  also  at  the  same  time  opened  their  eyes  to  the  magni- 
tude of  the  task  still  before  them ;  hence  the  reduction  in 
value  to  correspond  to  the  new  forecast  of  the  future. 

No  one  will  dispute  that  the  buyer  of  any  article  of  capital 
will  value  it  for  its  expected  services  to  him,  and  that  "  at 
the  margin"  of  his  purchases,  the  price  he  will  pay  is  the 
equivalent  to  him  of  those  expected  services,  or,  in  other 
words,  is  their  " present  worth,"  their  "discounted  value  " 
or  "capitalized  value."  But  some  doubt  may  be  felt  re- 
garding the  professional  seller.  As  to  him,  he  is  simply  a 
speculator  as  to  the  possible  demand.  He  sells  for  what  he 
can  get,  affixing  whatever  price  he  believes  will,  in  the  end, 
profit  him  most,  sometimes  making  out  of  the  transaction 
more  than  his  costs  of  acquisition,  sometimes  less,  usually,  or 
normally,  covering  those  costs  plus  interest  on  them  for  the 
time  elapsing  between  their  occurrence  and  the  sale. 

The  same  principle  applies  all  the  way  back  in  the  pro- 
duction processes.  The  labor  expended  is  staked  (either  by 
the  laborer  or  entrepreneur)  in  anticipation  of  the  prices 
which  the  buyers  will  be  willing  to  pay.  If  these  anticipated 
prices  are  not  expected  to  cover  the  value  of  the  labor  and 
other  costs  plus  the  interest  upon  them,  the  result  will  be 
that  the  labor  and  other  costs  will  not  be  expended.  Hence 
by  trial  and  error  the  labor  and  other  costs  will,  under  nor- 
mal conditions,  gradually  be  fitted  to  the  prices. 

When  prices  find  this  normal  level  at  which  costs  plus 
interest  are  covered,  it  is  not  because  the  past  costs  of  pro- 
duction have  determined  prices  in  advance,  but  because 


190  NATURE   OF   CAPITAL   AND   INCOME          [CHAP.  XI 

the  sellers  have  been  good  speculators  as  to  what  prices 
would  be.  If  they  had  foreseen  that  prices  would  not  cover 
costs  and  interest  on  costs,  they  would  have  refrained  from 
production  entirely,  while  if  they  had  foreseen  the  opposite 
condition,  that  of  large  profits,  competition  would  have 
tended  to  reduce  these  profits  to  the  usual  dimensions. 

We  see,  then,  that  although  prices  bear  a  normal  relation 
to  past  costs,  this  relation  does  not  always  hold  true ;  and 
that,  whether  it  holds  true  or  not,  the  costs  do  not  prede- 
termine the  prices  except  in  the  sense  that  the  producers 
have  skillfully  adapted  the  stocks  available  now,  and  those 
to  be  available  at  succeeding  points  of  time,  to  the  expected 
demand  for  them. 

It  is  not  our  purpose  in  the  present  book,  however,  to 
emphasize  these  principles,  for  they  belong  properly  to  the 
theory  of  prices.  We  merely  premise  them  in  order  to 
proceed  to  the  study  of  the  relation  between  capital-value 
and  income-value,  that  is,  of  what  we  have  called  "  value- 
re  turn." 


CHAPTER  XII 

CONCEPT  OF  RATE  OF  INTEREST 
§1 

FROM  the  last  chapter  we  obtained  the  concept  of 
value-return.  This  may  be  explicitly  defined  as  the  ratio 
of  the  value  of  the  income  which  flows  from  a  specified 
capital  during  a  specified  interval  of  time,  to  the  value  of 
that  capital  at  a  specified  point  of  time.  Thus,  if  on  Janu- 
ary 1,  1900,  a  capital  is  worth  $10,000,  and  during  the  year 
1900  this  capital  yields  an  income  worth  $500,  the  value- 
return  is  five  per  cent  per  annum  for  that  year.  If  the  in- 
come is  perpetual  and  flows  at  a  uniform  rate,  the  value- 
return  is  called  the  rate  of  interest  realized  on  the  capital.  In 
other  words,  the  rate  of  interest  is,  briefly  stated,  the  ratio 
between  income  and  capital.  As  business  men  say,  the  rate 
of  interest  is  the  "  price  of  money,"  or  the  "  price  of  capital." 
This  very  common  usage  is  based  on  the  thought  that  any 
capital  sum  is  the  equivalent  of  some  annuity.  The  usage 
has  been  needlessly  condemned  by  economists  on  the 
ground  that  a  different  meaning  should  be  assigned  to  the 
expression  "price  of  money,"  viz.  its  " purchasing  power" 
over  goods  in  general.  But  the  objection  is  not  well 
founded,  for  it  is  evident  that  " purchasing  power"  includes 
not  only  purchasing  power  over  a  stock  of  goods  but  also 
purchasing  power  over  a  flow  of  income.  If  $100  will  buy 
a  perpetual  annuity  of  $6  a  year  in  Japan,  while  in  England 
it  will  buy  one  of  only  $3  a  year,  the  purchasing  power  of 
capital  over  income  is  six  per  cent  in  Japan,  and  only  half  as 
much  in  England.  A  millionaire  in  the  first  country  will  be 
able  to  command  an  income  of  §60,000  without  trenching  on 

191 


192  NATURE   OF   CAPITAL   AND    INCOME         [CHAP.  XII 

his  capital,  whereas  in  England  he  can  get  but  $30,000,  and 
will,  therefore,  be  just  half  as  wealthy  in  actual  income. 


The  rate  of  interest  has  many  meanings,  and  since  the 
concept  is  so  vital  to  our  study,  we  shall  specify  carefully, 
in  the  present  chapter,  what  these  various  meanings  are. 
The  meaning  implied  in  the  previous  section  postulates  the 
existence  of  a  perpetual  annuity,  i.e.  a  uniform  and  per- 
petual flow  of  income.  Although  such  an  annuity  does 
not  actually  exist,  it  is  often  convenient  to  employ  it  as 
a  vehicle  of  thought.  Suppose  $10,000  to-day  will  secure 
a  perpetual  annuity  of  $400  per  year  payable  annually, 
the  first  payment  accruing  one  year  from  the  day  of  pur- 
chase ;  then  the  rate  of  interest  is  said  to  be  four  per  cent 
per  annum  payable  annually;  that  is,  the  rate  of  interest 
(when  the  interest  is  payable  annually)  is  the  ratio  between 
the  rate  of  flow  of  a  perpetual  annuity  and  its  equivalent  in 
present  capital. 

In  case  the  income  accrues  semi-annually  the  case  is 
slightly  different.  Let  $10,000  to-day  yield  a  perpetual  an- 
nuity of  $400  a  year  in  semi-annual  payments  of  $200  each, 
the  first  payment  being  due  six  months  from  date.  Then 
the  rate  of  interest  is  said  to  be  four  per  cent  per  annum 
payable  semi-annually. 

That  these  four-per-cent  rates  are  not  equivalent  to 
each  other  is  well  recognized  in  practice,  and  can  be  made 
evident  in  various  ways.  The  holder  of  the  semi-annual 
annuity  has  a  slight  advantage  over  the  holder  of  the  annual 
annuity,  because  he  receives  half  of  each  year's  income 
six  months  earlier.  He  may,  in  fact,  convert  his  income 
of  $200  twice  a  year  into  an  income  of  $404  once  a  year  ; 
for  in  six  months,  besides  receiving  his  first  installment  of 
$200,  he  may  receive  $10,000,  by  selling  his  annuity.  He 
may  then  reinvest  the  entire  $10,200  on  the  original  terms, 
4  per  cent  payable  semi-annually,  and  hence  obtain  a  per- 


SEC.  2]  CONCEPT   OF   RATE    OF    INTEREST  193 

pctual  annuity  of  $408,  in  semi-annual  installments  of  $204. 
In  six  months  more,  or  one  year  from  the  original  invest- 
ment, he  may  realize  $204  of  income  and  $10,200  of  "  prin- 
cipal," or  $10,404  in  all.  Of  this  he  may  reinvest  the 
original  $10,000,  retaining  $404.  From  this  point  onward 
he  may  repeat  the  same  annual  cycles  of  sales  and 
reinvestments,  and,  therefore,  receive  $404  net,  payable 
once  a  year.  He  is,  consequently,  better  off  by  $4  a  year, 
than  the  holder  of  an  annuity  of  $400  a  year,  payable 
annually.  In  other  words,  a  rate  of  interest  of  4  per  cent 
per  annum,  if  the  income  is  payable  semi-annually,  is 
equivalent  to  a  rate  of  interest  of  4.04  per  cent  per 
annum,  if  the  income  is  payable  annually. 

The  same  reasoning  may  be  applied  when  the  income 
accrues  at  quarterly  or  any  other  intervals.1 

By  subdividing  the  time  of  payment  indefinitely,  we  may 
pass  from  an  income  obtained  in  installments  to  a  continu- 
ous flow  of  income.  The  idea  of  a  uniform  and  perpetual 
stream  of  income  is  nearly  realized  in  certain  cases,  as  in  the 
West,  where  water  rights  are  sometimes  bought  in  the  form 
of  a  "miner's  inch"  —a  perpetual  flow  through  a  square 
inch  opening  under  a  head  of  six  inches.  Let  us  suppose 
that  the  water  is  worth  $100  a  year.  If  the  right  to  such 
a  perpetual  and  uniform  flow  can  be  bought  for  $2000,  the 
rate  of  interest  is  five  per  cent  "reckoned  continuously." 

We  thus  reach  the  conclusion  that  there  are  various 
senses  of  the  rate  of  interest,  according  to  the  frequency 
of  payment,  namely,  — 

The  rate  of  interest  per  annum,  income  payable  annually. 

The  rate  of  interest  per  annum,  income  payable  semi-annually. 

The  rate  of  interest  per  annum,  income  payable  quarterly. 

The  rate  of  interest  per  annum,  income  payable  at  other  intervals. 

The  rate  of  interest  per  annum,  income  payable  continuously. 

The  last  named,  while  it  is  the  least  familiar  in  practice,  is  in 

some  respects  the  most  natural,  and  lends  itself  the  most 

1  See  Appendix  to  Chap.  XII.  §  1. 


194  NATURE   OF   CAPITAL   AND   INCOME        [CHAP.  XII 

readily  to  mathematical  transformations.  The  first,  on  the 
other  hand,  is  the  most  frequently  used  in  practical 
computations. 

§o 
3 

We  have  considered  the  rate  of  interest  as  the  price  of 
capital  in  terms  of  income.  If  we  consider  reciprocally 
the  price  of  income  in  terms  of  capital,  we  shall  have  what 
is  called  the  "rate  of  capitalization."  It  is  measured  in 
years,  namely,  the  number  of  years  during  which  there 
would  flow  an  amount  of  income  equal  to  the  capital.  Thus, 
if  $25,000  will  buy  a  perpetual  annuity  of  $1000  a  year,  the 
rate  of  capitalization  is  "  twenty-five  years'  purchase."  The 
concept  of  "  years'  purchase "  is  common  in  England  as 
applied  to  land  rents.  It  is  evidently  interconvertible  with 
the  rate  of  interest.  A  rate  of  interest  of  four  per  cent  indi- 
cates a  "years'  purchase"  or  rate  of  capitalization  of 
twenty-five  years.  A  rate  of  interest  of  two  per  cent 
indicates  a  rate  of  capitalization  of  fifty  years.  The  rate  of 
capitalization  has  thus  as  many  meanings  as  the  rate  of 
interest,  according  as  the  income  is  payable  annually, 
semi-annually,  quarterly,  etc.,  or  continuously. 


The  concepts  of  interest  which  have  been  given  depend 
upon  the  concept  of  a  perpetual  annuity.  But  they  can  be 
made  to  apply  also  to  terminable  annuities.  Thus,  $10,000 
may  yield  at  four  per  cent  an  income  of  $400  a  year  for 
ten  years,  at  the  expiration  of  which  time  the  $10,000,  or 
the  "original  loan,"  is  returned.  In  such  a  case  the  loan 
may  evidently  be  regarded  as  a  purchase  and  resale  of  a 
perpetual  annuity.  A  perpetual  annuity  of  $400  is,  for  the 
price  of  $10,000,  diverted  to  the  lender's  benefit,  and  at  the 
end  of  ten  years  is  restored  to  the  borrower  for  the  same 
sum. 

We  may  regard  in  this  light  even  short-time  loans.     Thus, 


SEC.  4]        CONCEPT  OF  RATE  OF  INTEREST          195 

if  a  man  borrows  $100  to-day  and  agrees  to  pay  it  back  with 
interest  at  4%  in  one  year,  we  may  conceive  of  him  as 
having  sold  a  perpetual  annuity  of  $4  a  year  for  $100,  and 
at  the  same  time  as  having  bound  himself  to  buy  it  back  for 
$100  at  the  end  of  one  year.  The  combined  result  of  these 
operations  amounts  to  an  exchange  of  $100  this  year  for 
$104  next  year.  It  is  possible  to  use  such  a  simple  exchange 
between  this  year's  and  next  year's  money,  as  the  basis  of 
an  entirely  new  definition  of  the  rate  of  interest,  and  one 
which  is  independent  of  the  idea  of  an  annuity.  When 
$100  to-day  is  exchanged  for  $104  next  year,  the  ratio  of 
exchange  between  the  two  sums  is  \%$.  This  ratio  is  not, 
of  course,  itself  the  rate  of  interest;  the  rate  of  interest  is 
the  excess,  or  premium,  of  y^,  above  unity.  In  other 
words,  the  rate  of  interest  is  the  premium,  or  "agio,"  above 
par  of  this  year's  dollars  in  terms  of  next  year's  dollars. 

Such  a  concept  of  interest  may  be  called  the  premium  con- 
cept, whereas  the  concept  hitherto  employed,  or  the  price  of 
capital  in  terms  of  an  annuity,  may  be  called  the  price  con- 
cept of  the  rate  of  interest.  To  say  that  the  rate  of  interest 
in  the  price  sense  is  four  per  cent  means  that  the  price  of  $100 
of  capital  is  $4  of  income  per  annum  forever.  To  say  that 
the  rate  of  interest  in  the  premium  sense  is  four  per  cent 
means  that  the  price  of  $100  of  one  year's  goods  is  $104  of 
the  next  year's  goods. 

The  premium  concept  of  the  rate  of  interest  has  been  so 
much  emphasized,  notably  by  Bohm-Bawerk,  that  it 
seems  advisable  to  repeat  briefly,  with  respect  to  it,  the  dis- 
tinctions as  to  annual,  semi-annual,  quarterly,  etc.,  reckon- 
ing. Let  us  suppose  that  $100  to-day  is  worth  $102  six 
months  hence.  The  rate  of  interest  in  the  premium  sense 
is  here  2  per  cent  for  the  six  months'  interval,  and  is  said 
to  be  "  4  per  cent  per  annum  payable  or  reckoned  semi-an- 
nually."  It  will  be  evident,  however,  that  this  is  a  little 
higher  rate  than  4  per  cent  per  annum  reckoned  annually. 
Let  us  suppose  that  at  the  end  of  six  months,  at  which  time 


196  NATURE   OF   CAPITAL   AND   INCOME        [CiiAP.  XII 

\ 

S102  is  due,  the  debt  is  renewed  for  another  six  months  at 
the  same  rate.  It  is  evident  that  the  $102  will  then,  by 
"compounding,"  amount  to  $102  x  1.02,  or  $104.04.  The 
interest  then,  at  the  end  of  a  year,  instead  of  being  $4,  is 
84.04.  In  other  words,  4  per  cent  interest  reckoned  half- 
yearly  is  equivalent  to  4.04  per  cent  reckoned  yearly,  as  was 
also  the  case  under  the  price  concept  of  the  rate  of  interest. 
In  the  same  way  we  may  consider  quarterly  or  other  inter- 
vals for  compounding.  At  the  limit,  the  interval  for  com- 
pounding may  be  reduced  to  an  instant.1 

We  have  then  two  methods  of  defining  interest.  In 
both  of  them  the  time  element  is  prominent.  Before  pass- 
ing on  we  should  here  remark  that  the  time  element  enters 
not  only  as  referring  to  the  times  of  payment  but  also  to 
the  time  of  contract.  A  rate  of  interest  implies  not  only 
the  two  points  of  time  between  which  the  goods  for 
exchange  are  available,  but  also  the  point  at  which  the  de- 
cision to  exchange  them  is  made.  It  would  be  quite  pos- 
sible, for  instance,  to  agree  in  the  year  1900  to  exchange 
$1000  in  the  year  1901  for  a  given  sum  or  series  of  sums 
returnable  at  still  later  dates.  In  this  case  the  rate  of 
interest  for  this  exchange  appertains  to  the  year  1900, 
although  execution  of  the  contract  does  not  begin  until  a 
year  later  and  is  not  concluded  until  later  still.  These 
conditions  have  often  been  overlooked  in  treating  statis- 
tics of  the  rate  of  interest. 

§5 

We  have  defined  the  rate  of  interest  both  in  the 
"price"  and  the  "premium"  sense.  The  question  now 
arises  whether  these  two  concepts  are  interchangeable. 
Under  certain  conditions  they  are,  and  under  others  they 
are  not.  Cases  in  which  the  two  are  interchangeable  are 
shown  in  the  following  propositions. 

1  For  the  mathematical  relations  involved,  see  Appendix  to  Chap. 
XII,  §  2. 


SEC.  5]  CONCEPT   OF   RATE   OF   INTEREST  197 

(1)  If  the  rate  of  interest,  in  the  sense  of  a  premium  on 
this  year's  goods  in  terms  of  next  year's  goods,  is  the  same 
year  after  year  forever,  then  the  rate  of  interest  considered 
as  the  price  of  capital  in  terms  of  a  perpetual  annuity  will  be 
equal  to  it. 

A  numerical  example  will  make  this  clear.  We  shall  sup- 
pose that  the  rate  of  interest  is  four  per  cent  in  the  premium 
sense,  i.e.  that  $100  at  any  moment  during  the  period  under 
consideration  will  buy  $104  to  be  paid  one  year  later.  We 
are  to  show  that  as  a  consequence  $100  will  necessarily  buy 
an  annuity  of  $4  a  year  forever.  Let  us  suppose,  then,  the 
premium  rate  being  4  per  cent,  that  $100  is  spent  for  $104, 
to  be  repaid  one  year  later.  Of  this  $104,  when  it  is 
received  at  the  end  of  the  year,  the  investor  reinvests  $100. 
By  our  hypothesis  of  an  unchanged  interest  rate,  this  $100 
will  bring,  at  the  end  of  the  second  year,  another  $104, 
of  which  in  turn  $100  is  reinvested ;  and  so  on  indefinitely. 
By  continually  reinvesting,  he  obtains  for  his  original  $100, 
$4  a  year  indefinitely  and  $100  deferred  indefinitely.  If 
the  process  is  perpetual,  the  $100  is  deferred  to  infinity, 
and  has  no  present  value.  Hence  the  original  $100  obtains 
simply  a  perpetual  annuity  of  $4  a  year,  and  the  rate  of  in- 
terest in  the  price  sense  is  therefore  also  4  per  cent,  which 
was  to  have  been  proved.1 

It  is  evident  that  this  reasoning  may  all  be  put  in  general 
terms,  and  that  it  applies  equally  to  interest  reckoned 
semi-annually,  quarterly,  etc.,  and  continuously. 

(2)  Conversely,  if  a  given  rate  of  interest  in  the  price 
sense  holds  good  to-day,  next  year,  two  years  later,  and  so 
on   indefinitely,  then  the  rate  of  interest  in  the  premium 
sense  will  be  equal  to  it. 

This  also  may  be  readily  shown  by  an  example.  If  $100 
will  buy  $4  a  year  forever,  the  first  $4  being  due  one  year 

1  An  alternative  proof  consists  in  obtaining  the  present  value  of 
each  successive  item  of  income  and  adding  the  results.  This  process 
is  exemplified  in  the  next  chapter  in  obtaining  the  capital-value  of  a 
perpetual  annuity. 


198  NATURE    OF   CAPITAL   AND   INCOME        [CHAP.  XII 

hence,  the  buyer  of  such  an  annuity  at  the  end  of  one  year 
may,  immediately  upon  the  receipt  of  his  first  $4,  sell  out 
his  rights.  By  hypothesis  they  will  bring  $100.  Conse- 
quently, he  receives  $104  in  all  for  his  $100  a  year  ago.  He 
has  thus  virtually  exchanged  $100  one  year  for  $104  the 
year  after.  That  is,  the  premium  rate  of  interest  for  this 
year  is  also  4  per  cent. 

We  see,  then,  that  if  the  rate  of  interest  in  either  of  the 
two  senses  —  price  or  premium  —  remains  constant,  the 
rate  in  the  other  sense  will  also  remain  constant  and  equal 
to  the  former. 

It  is  clear  that  the  same  reasoning  applies  to  interest 
reckoned  for  any  period  of  time,  —  semi-annually,  quar- 
terly, continuously. 

But  if  the  rate  of  interest  does  not  remain  constant,  its 
two  senses  of  price  and  premium  are  no  longer  interchange- 
able. Thus,  suppose  that  the  rate  is  4  per  cent  in  the 
premium  sense  for  the  first  year,  but  3  per  cent  for  the 
second  year  and  for  all  succeeding  years.  This  means  that 
$100  to-day  will  buy  $104  next  year,  and  that  $100  next  year 
will  buy  $103  the  year  after.  Then  $100  to-day  will  evi- 
dently not  buy  $4  a  year  forever,  nor  $3,  but  an  intermediate 
amount,  approximately  $3.03,  so  that  the  rate  of  interest  in 
the  price  sense  is  3.03  per  cent.1 

Again,  suppose  that  the  rate  of  interest  in  the  price  sense 
is  4  per  cent  this  year,  but  3  per  cent  next  year.  This 
means  that  $100  to-day  will  buy  $4  a  year  forever,  and 
that  $100  next  year  will  then  buy  $3  a  year  forever. 
Then  $100  to-day  will  not  buy  $104  next  year,  nor  $103, 
but  $137^.  That  is,  the  rate  of  interest  in  the  premium  sense 
is  37^  per  cent.2  Thus  a  very  slight  change  in  the  price  rate 
of  interest  implies  a  great  change  in  the  premium  rate  of  in- 

1  Roe  Appendix  to  Chup.  XII,  §  3. 

2  See  Appendix  to  Chap.  XII,  §  4. 


SEC.  7]  COXCKPT   OF    RATK    OF    IXTKRKST  199 

terest.  This  goes  to  explain  why,  in  the  actual  market,  the 
rate  of  interest  for  short-time  loans  fluctuates  so  much 
more  widely  than  the  rate  of  interest  on  long-time  invest- 
ments. It  is  scarcely  necessary  to  exhibit  statistics  to  show 
this,  though  they  are  easily  obtained  by  comparing  the 
fluctuations  in  the  rate  of  interest  on  short-term  and  long- 
term  loans,  in  the  United  States  or  in  England. 

We  see,  then,  that  the  two  concepts  of  interest  rate,  though 
definitely  related/  are  not  always  interchangeable. 

§7 

There  is  yet  another  device  for  indicating  the  terms  of 
time  exchanges.  Besides  the  rates  of  interest  and  their 
reciprocals,  the  ratios  of  capitalization,  there  is  the  rate  of 
discount.  We  have  seen  that  if  $104  due  one  year  hence 
will  buy  $100  of  present  goods,  then  -]-§-£  is  the  rate  of  ex- 
change between  the  two  times  and  exceeds  unity  or  par  by 
Y^-JJ,  the  rate  of  interest.  The  rate  of  exchange  between  the 
two  times,  when  taken  in  the  opposite  direction,  is  \-^  and 
this  is  less  than  unity  or  par  by  T^?.  This  deficiency, 
which  amounts  to  3.9  per  cent,  is  called  the  rate  of  discount. 
The  number  representing  the  rate  of  discount  is  always 
slightly  less  than  that  representing  the  corresponding  rate 
of  interest.2  The  rate  of  discount  is  practically  employed 
only  for  short-time  loans,  usually  less  than  a  year,  in  which 
cases  it  better  serves  the  purposes  of  rapid  computation. 

§8 

The  present  chapter  may  be  briefly  summarized  as  fol- 
lows :  — 

First,  the  rate  of  interest  is  a  special  case  of  ''value- 
return,'7  and  may  be  approached  from  either  of  two  stand- 
points, according  as  we  consider  it  the  price  of  capital  in 

1  See  Appendix  to  Chap.  XII,  §  5. 

2  For  further  discussion  of  the  rate  of  discount,  see  Appendix  to 
Chap.  XII,  §§  6,.  7. 


200 


NATURE   OF   CAPITAL   AND   INCOME        [CHAP.  XII 


terms  of  a  perpetual  annuity,  or  the  premium  on  the  price 
of  this  year's  goods  in  terms  of  next  year's  goods.  These 
two  definitions  of  the  rate  of  interest  we  have  found  to  be 
interchangeable  when  either  one  of  them  is  assumed  to  be 
invariable ;  but  when  this  condition  is  not  fulfilled  the  two 
are  not  interchangeable. 

Secondly,  not  only  does  the  rate  of  interest  have  the  two 
distinct  meanings  which  have  been  given,  but  each  mean- 
ing is  subject  to  various  interpretations,  according  as  the 
interest  is  payable  or  reckoned  annually,  semi-annually, 
quarterly,  etc.,  or  continuously. 

Thirdly,  as  alternatives  to  the  rate  of  interest  we  may  em- 
ploy the  rate  of  discount  and  the  rate  of  capitalization. 
Both  of  these  magnitudes  also  apply  either  in  the  price  sense 
or  the  premium  sense.  Furthermore,  like  the  rate  of  in- 
terest, they  apply  somewhat  differently  according  as  the 
reckoning  is  annual,  semi-annual,  quarterly,  etc.,  or  con- 
tinuous. 

The  following  table  illustrates  the  various  magnitudes 
which  have  been  considered : 1  — 

EQUIVALENT  RATES   OF   INTEREST,  DISCOUNT,  AND  CAPITALIZATION 


A 

B 

C 

D 

Reciprocal 

Rate  of 

Rate  of 

of  A,  or 

Recipro- 

Interest 

Discount 

Rate  of 

cal  of  B 

Capitalization 

Reckoned  annually     .     . 

4.00% 

3.85% 

25.0  yrs. 

26.0  yrs. 

Reckoned  semi-annually 

3.96% 

3.88% 

25.3  vrs. 

25.8  yrs. 

Reckoned  quarterly    .     . 

3.94% 

3.90% 

25.4  yrs. 

25.6  yrs. 

Reckoned  continuously 

3.92  % 

3.92% 

25.6  yrs. 

25.6  yrs. 

Since  the  sixteen  magnitudes  in  this  table  may  be  taken 
either  in  the  price  or  the  premium  sense,  and  since,  when  in- 

1  For  their  mathematical  "  dimensions,"  see  Appendix    to   Chap. 
XII,  §8. 


SEC.  8]        CONCEPT  OF  RATE  OF  INTEREST         201 

constancy  enters,  the  two  senses  will  involve  two  unequal 
magnitudes,  we  have  here  represented  or  implied  thirty- 
two  possible  magnitudes.  The  means  for  expressing  time 
exchanges  between  goods  of  the  same  kind  thus  present 
an  embarrassing  variety.  But  since  it  is  easy  to  proceed 
from  any  one  of  them  to  all  the  others,  it  is  evident  that  we 
need  not,  in  general,  employ  more  than  one.  The  one 
which  is  practically  the  simplest,  and  which,  therefore,  we 
shall  hereafter  employ  in  this  book  is:  the  rate  of  interest 
per  annum  reckoned  annually  and  considered  as  a  premium 
on  the  goods  of  one  year  compared  with  those  of  the  year  follow- 
ing. 


CHAPTER  XIII 

VALUE    OF   CAPITAL 


HAVING  found  what  constitutes  a  rate  of  interest,  we  are 
now  enabled  to  pursue  our  study  of  the  relation  between 
capital  and  income.  We  found  in  Chapter  XI  that  these  rela- 
tions are  of  four  kinds,  according  to  whether  the  income 
and  the  capital  are  measured  in  quantity  or  in  value.  The 
fourth  of  these,  "  value-return,"  brought  us  to  the  concept 
of  a  rate  of  interest. 

The  rate  of  interest  acts  as  a  link  between  income-value 
and  capital-value,  and  by  means  of  this  link  it  is  possible 
to  derive  from  any  given  income-value  its  capital-value,  i.e. 
to  "capitalize"  income. 

To  do  this,  we  assume  that  the  expected  income  is  fore- 
known with  certainty,  and  that  the  rate  of  interest  (in  the 
sense  of  an  annual  premium)  is  foreknown,  and  also  that  it 
is  constant  during  successive  years.  With  these  provisos 
it  is  very  simple  to  derive  the  capital-value  of  the  income  to 
be  yielded  by  any  article  of  wealth  or  item  of  property;  in 
other  words,  to  derive  the  value  of  that  wealth  or  prop- 
erty. That  value  is  simply  the  present  worth  of  the  future 
income  from  the  specified  capital.  This  is  true  whether 
the  income  accrues  continuously  or  discontinuously ; 
whether  it  is  uniform  or  fluctuating;  whether  the  install- 
ments of  income  are  few  or  infinite  in  number. 

We  begin  by  considering  the  simplest  case,  that,  namely, 
in  which  the  future  income  consists  of  a  single  item  accru- 
ing at  a  definite  instant  of  time.  If,  for  instance,  one  holds 
a  property  right  by  virtue  of  which  he  will  receive,  at  the  end 

202 


SEC.  1]  VALUK    OF   CAPITAL  203 

of  one  year,  the  sum  of  $104,  the  present  value  of  this 
right,  if  the  rate  of  interest  is  4  per  cent,  will  be  $100. 
If  the  property  is  the  right  to  $1  one  year  hence,  its  present 
value  is  evidently  j.U4  or  $0.902,  and  if  the  sum  to  which  the 
property  entitles  the  owner  is  any  other  amount  than  $1, 
its  present  value  is  simply  that  amount  divided  by  1.04 
or  multiplied  by  .962.  Thus  the  present  value  of  $432 
due  in  one  year  is  ^,  or  432  x  .902,  which  is  $416. l 

If  the  future  sum  is  due  in  two  years,  and  the  rate  of 
interest  is  still  4  per  cent,  it  is  evident  that  $1  to-day  is 
the  present  value  of  $1.04  next  year,  which  in  turn  (by 
compounding)  will  then  be  the  present  value  of  $1.04  x  1.04 
(?:.  e.  [1.04] 2,  or  $1.082)  at  the  end  of  the  second  year.  The 
$1.082  is  called  the  "amount"  of  $1  at  the  end  of  two 
years,  and  $1.04  is  the  " amount"  of  $1  in  one  year. 

Similarly,  in  three  years  (1.04)3  is  the  "amount"  or  sum 
worth  $1  in  present  value;  and  so  on  for  any  number  of 
years.  These  results  show  what  $1  to-day  is  worth  at 
the  end  of  any  number  of  years.  And  conversely,  from 
them  it  is  easy  to  see  what  $1  due  at  the  end  of  any  number 
of  years  is  worth  to-day.  We  have  already  seen  that  the 
present  worth  of  $1  due  in  one  year  is  — ,  or  $0.962. 
Similarly,  the  present  value  of  $1  due  at  the  end  of  two, 
three,  etc.,  years  is  respectively  ^j^,  aT^ys,  etc.2  Knowing 
the  present  value  of  $1,  we  may  evidently  find  that  of  any 
other  sum  by  simple  proportion. 

To  illustrate  these  results  geometrically,  let  us  represent 
time  by  horizontal  lines,  and  the  value  of  the  capital  by 
vertical  lines;  then  the  curve  A  A'  A"  A'" ,  as  shown  in 
Figure  1,  will  exhibit  the  relative  values  at  any  two  in- 
stants, exchangeable  on  the  basis  of  a  given  rate  of  interest, 
compounded  annually. 

The  point  B  represents  the  present  instant;   Bf,  the  in- 

1  For  the  general  mathematical  treatment,  see  Appendix  to  Chap. 
XIII,  §  1. 

2  For  a  mathematical  formulation,  see  Appendix  to  Chap.  XIII,  §  2. 


204 


NATURE   OF   CAPITAL   AND   INCOME      [CHAP.  XIII 


slant  a  year  hence;  B" ,  that  two  years  hence;  B'" ,  three 
years  hence;  and  B(t\  t  years  hence.  AB  represents  any 
present  value,  A'B'  the  "amount  "of  this  sum  one  year  hence, 
A"B"  the  "amount"  two  years  hence,  etc.  Consequently, 
AB  also  represents  the  present  value  of  A'BT  due  one  year 
hence,  or  of  A"B"  due  two  years  hence,  or  of  AWBW  due 
t  years  hence.  The  curve  A  AM  is  an  "  exponential  curve," 
this  being  the  name  given  to  a  curve  which  ascends  in  geo- 


BUI 


FIG.  1. 


metrical  progression,  i.e.  ascends  so  that  the  successive 
vertical  lines,  AB,  A'B',  A"B",  andA"'£m(ordinates), 
taken  at  equal  intervals,  increase  in  length  at  a  uniform 
ratio.  We  shall,  however,  for  economic  purposes,  christen 
this  curve  the  "discount  curve." 

§2 

The  principles  which  have  been  explained  for  obtaining 
the  present  value  of  a  single  future  sum  apply  to  many 
commercial  transactions,  especially  to  the  valuation  of  bank 
assets,  which  exist  largely  in  the  form  of  "discount  paper," 
or  short-time  loans  of  other  kinds.  The  principles  also 
apply,  though  in  combination  with  those  of  risk  and  for- 
eign exchange,  to  that  form  of  property  called  "bills  of 


SEC.  2]  VALUIC    OF   CAPITAL  205 

exchange."  Still  another  application  is  to  wealth  which  is 
in  course  of  trade  and  of  which,  therefore,  the  only  service 
to  the  owner  consists  in  its  sale.  It  is  on  this  principle 
that  a  dealer  reckons  the  value  of  his  stock,  by  discount- 
ing its  selling  price  for  the  time  which  will  probably  elapse 
before  it  is  sold  —  deducting,  of  course,  the  prospective 
expense  of  selling,  discounted  in  like  manner.  Similarly,  the 
value  of  any  article  of  wealth  reckoned  when  that  wealth 
is  in  course  of  construction  is  the  present  value  of  what  it 
will  bring  when  completed,  less  the  present  value  of  the 
cost  of  completion.  For  instance,  the  maker  of  an  auto- 
mobile will  appraise  it,  at  any  of  its  stages  in  course  of 
construction,  as  worth  the  discounted  value  of  its  probable 
return  when  subsequently  finished  and  sold,  less  the  dis- 
counted value  of  the  costs  of  construction  and  selling 
which  still  remain.  Of  course,  the  element  of  risk  cannot, 
in  such  cases,  be  overlooked ;  but  its  consideration  belongs 
to  a  later  chapter. 

Another  application  of  these  principles  of  capitalization 
is  to  goods  in  transit.  A  cargo  leaving  S}'dney  for  Liv- 
erpool is  worth  the  discounted  value  of  what  it  will  fetch 
in  Liverpool,  less  the  discounted  value  of  the  cost  of  carry- 
ing it  there.  Other  classical  examples  are  wine,  the  value 
of  which  is  the  present  worth  of  what  it  will  be  when 
"mellow"  and  ready  for  consumption;  and  young  forests, 
which  are  worth  the  discounted  value  of  the  lumber  they 
will  ultimately  form.  In  Germany  and  some  other  coun- 
tries, such  appraisement  of  forests  is  now  worked  out  with 
considerable  precision. 

§3 

It  seldom  happens,  however,  that  there  is  one  item  only  of 
income  or  outgo  earned  by  an  article  of  capital.  The  items 
are  unusually  numerous.  Perpetual  annuities,  for  in- 
stance, form  an  important  class,  in  which  these  items  recur 
in  equal  amounts  and  during  equal  intervals  forever.  We 


206  NATURE    OF   CAPITAL   AND   INCOME       [CHAP.  XIII 

have  already  seen,  in  the  last  chapter,  that  if  a  person  owns 
the  right  to  $1  a  year  payable  at  annual  intervals  forever, 
its  present  value,  reckoned  at  four  per  cent,  is  ~-v  or  §25. 
If  his  annuity  is  32  per  year,  its  present  value  is  evidently 
double  this,  or  $50;  and  if  it  is  any  other  sum,  its  present 
value  is  found  by  multiplying  in  the  same  way.  Thus,  an 
annuity  of  $17  is  worth  |].  In  other  words,  the  value  of  a 
perpetual  annuity  is  found  by  dividing  the  annual  income 
by  the  rate  of  interest,1  or,  what  amounts  to  the  same  thing, 
by  multiplying  the  income  by  the  rate  of  capitalization, 
also  called  the  number  of  years'  purchase.  This  proposi- 
tion, however,  serves  to  determine  only  that  capital-value 
which  an  annuity  possesses  at  its  inception  (i.e.  one  year 
before  the  first  installment)  or  at  any  other  point  taken 
one  year  in  advance  of  the  first  of  the  installments  to  be 
included  in  the  calculation.  The  value  of  the  annuity, 
taken  immediately  before  any  installment  of  income  falls 
due,  is  evidently  greater  than  the  above,  by  the  amount 
of  that  installment.  Thus,  if  the  rate  of  interest  is  four 
per  cent,  a  perpetual  annuity  of  $4  a  year,  of  which  the 
first  payment  falls  due  one  year  hence,  is  worth  $100  to- 
day, and  is  also  worth  this  same  sum  at  any  instant 
immediately  following  the  payment  of  an  installment. 
But  next  year,  immediately  before  the  first  payment 
becomes  due,  it  will  be  worth  $104.  At  any  intermediate 
point  between  the  present  when  it  is  worth  $100  and  a 
year  hence  when  it  is  worth  $104,  it  will  be  worth  an 
intermediate  amount,  determined  by  the  discount  curve; 
for  its  value  will  always  be  the  discounted  value  of  the 
$104,  which  could  be  realized  on  it  at  the  time  of  the  next 
interest  payment.  As  soon  as  this  payment  has  passed  by, 
the  value  will  drop  to  $100  again,  after  which  it  will  gradu- 
ally ascend  as  before,  and  so  on,  following  a  series  of  curves 
like  the  teeth  of  a  saw,  as  shown  in  Figure  2.  In  this 
diagram,  the  value  of  the  annuity  is  represented  by  suc- 
1  For  a  mathematical  statement,  see  Appendix  to  Chap.  XIII,  §  3. 


SEC.   3] 


VALUi:    OF    CAPITAL 


207 


cessive  vertical  linos,  four  units  in  height,  each  representing 
$4,  and  situated  one  unit  of  time  apart.1 

If  the  annuity  is  "deferred,"  i.e.  does  not  begin  till  some 
future  time,  its  present  value  is  the  discounted  value  of 


that  value  it  will  possess  when  it  docs  begin.  Thus,  in- 
terest being  four  per  cent,  Avhile  $100  is  the  value  of  a  $4 
annuity  beginning  to-day  (by  which,  as  we  have  seen,  is 
meant  that  its  first  installment  falls  due  one  yer.r  from 
to-day),  the  present  value  of  an  annuity  deferred  one  year 
later  will  be  only  ^,  or  $96.15.  and  the  present  value  of  an 
annuity  deferred  five  years  is  -(1lf^7iJ  or  892.46.  The  value 
of  the  annuity  at  any  time  before  its  inception  at  the  point 
A  is  shown  by  the  height  at  any  point  of  the  discount 
curve  through  .4. 

In  the  preceding  discussion,  the  income,  which  is  sup- 
posed to  accrue  in  installments,  is  represented  by  separate 
successive  vertical  line*.  But  when  the  income  is  sup- 
posed to  flow  continuously,  it  becomes  necessary  to  repre- 
sent it  bv  an  area.  In  the  '''area''  method,  time  is  still 


1  For  further  discussion  of  the  effect  of  reckoning  interest  for  dif- 
ferent time-intervals,  see  Appendix  to  Chap.  XIII,  §  4. 


208 


NATURE   OF   CAPITAL   AND   INCOME      [CHAP.  XIII 


represented  by  horizontal  lines,  and  vertical  lines  or  orcli- 
nates  are  employed  —  not  to  represent  income,  but  rate  of 
income.  Thus,  in  Figure  3,  AC  is  the  rate  of  income  flow- 
ing at  the  instant  A,  and  BD  is  the  rate  at  the  instant  B. 


FIG.  3. 

As  a  consequence,  the  income  which  flows  through  any 
period  of  time,  AB,  is  represented  by  the  area  ABDC.  It 
is  therefore  the  time  AB  multiplied  by  the  average  rate. 
In  the  case  of  a  uniform  flow  of  income,  CD  reduces  to  a 
horizontal  straight  line.  The  area  method  will  hereafter 
be  used  wherever  continuous  income  is  in  question.1 

§4 

Actual  examples  of  true  perpetual  annuities  cannot  be 
said  to  exist ;  but  for  practical  purposes,  some  government 
"rentes"  are  perpetual  annuities,  also  railway  leases  for 
999  years.  While  the  capital  value  of  a  perpetual  annuity 
of  $4  a  year,  capitalized  at  4  per  cent,  is  $100,  that  of  an 
annuity  of  §4  a  year  for  50  years  is  $85,  for  75  years  is  $94, 
for  100  years  $98,  and  for  200  years  $99.90.  It  will  be  seen, 
therefore,  that  for  any  ordinary  rate  of  interest,  an  annuity 
extending  a  century  or  more  is  practically  equal  in  value  to 
a  perpetual  annuity. 

Among  non-monetary  examples  may  be  cited  as  per- 
petual annuities  the  before-mentioned  water  rights  in  the 
West.  These  are  often  sold  by  the  miner's  inch,  i.e.  a 
theoretically  perpetual  flow  of  1^  cubic;  feet  per  minute, 

1  For  a  fuller  statement  of  the  area,  method,  as  related  to  the  line 
method,  see  Appendix  to  Chap.  XIII,  §  5. 


SEC.  5]  VALUK    OF    CAPITAL  209 

which  is  supposed  to  he  the  rate  at  which  water  will  flow 
through  an  aperture  of  one  square  inch  with  a  "head" 
of  six  inches.  The  "first"  inches  are  often  so  sure  to  con- 
tinue as  to  be  guaranteed.  Again,  if  we  overlook  the 
element  of  risk,  the  hares  in  joint  stock  companies 
often  exemplify  perpetual  annuities. 

Turning  from  capital  proper  y  to  capital  wealth,  we  find 
in  land  an  approximate  example  of  capital  yielding  a  per- 
petual annuity.  Land  is  often  capitalized  on  the  basis  of  a 
perpetual  and  uniform  income,  in  the  form  of  crops  or  other 
uses.  It  is  then  valued  at  a  certain  number  of  years'  pur- 
chase. These  so-called  "natural  and  indestructible  powers 
of  the  soil/'  however,  which  such  a  calculation  assumes,  do 
not  always  exist,  and  when  they  do  exist,  do  not  always 
yield  a  perpetual  annuity.  Mines  and  quarries  become 
exhausted,  while  much  land  yields  an  irregular,  increasing, 
or  decreasing  income  stream. 

§  5 

We  turn  now  from  perpetual  to  terminable  annuities. 
Suppose  that  a  man  possesses  a  ten-year  annuity  of  $100  a 
year.  This  means  that  he  has  the  right  to  receive  ten  annual 
payments  of  S100  each,  the  first  falling  due  one  year  from 
the  present  moment.  It  is  clear  that  such  an  annuity  differs 
from  a  perpetual  one  by  lacking  the  infinite  succession  of 
payments  after  the  ten  years  are  past.  In  short,  the 
terminable  annuity  is  simply  a  perpetual  annuity  dated 
to-day,  less  a  perpetual  annuity  deferred  ten  years.  There- 
fore, the  present  value  of  the  terminable  annuity  is  simply 
the  difference  between  the  present  value  of  the  two  perpet- 
ual annuities.  Of  these  two  perpetual  annuities,  the  pres- 
ent value  of  the  one  which  begins  immediately,  interest 
being  four  per  cent,  is  82500,  and  that  of  the  one  which  is 
deferred  ten  years  is  fj^,  or  S16S9.  Their  difference  is 
S2500-S1689  or  811.  Now  such  a  difference  as  this,  i.e. 
the  difference  between  any  particular  sum  (as  $2500)  and 


210  NATURE    OF    CAPITAL   AND    INCOME      [CiiAP.  XIII 

its  discounted  value  for  any  time,  is  called  the  total  discount 
on  that  sum.  We  may,  therefore,  express  our  result  by 
saying  that  the  present  value  of  a  terminable  annuity  is  the 
total  discount  on  a  perpetual  annuity  of  the  same  annual 
amount  beginning  when  the  terminable  one  ends.1 

If  the  terminable  annuity  is  itself  deferred,  its  present 
value  is  the  discounted  value  of  its  value  reckoned  at 
inception. 

§6 

Terminable  annuities  are  sometimes  employed  by  insur- 
ance companies  and  governments,  but  are  otherwise  com- 
paratively rare  as  specific  forms  of  property  rights.  Ap- 
proximate cases,  however,  of  such  income  exist  in  the  case 
of  many,  if  not  most,  durable  articles  of  wealth.  Thus,  a 
machine  yields  a  series  of  services  of  fairly  uniform  value  for 
a  fairly  fixed  term  of  years,  and  the  same  may  be  true  of  a 
house  or  other  building,  a  ship,  the  rolling  stock  and  other 
equipment  of  a  railroad,  etc.  Such  terminable  income  is 
also  exemplified  in  many  kinds  of  land,  in  the  case  of  mines 
and  quarries,  peat  beds  and  other  tracts  whose  yield  brings 
exhaustion.  The  state  of  Nevada  presents  an  example  of 
a  large  area  of  land  which  once  yielded  large  incomes,  but 
to-day  is  quite  or  nearly  unproductive.  It  is  evident, 
however,  that  in  all  these  cases  risk  is  an  important  factor 
in  determining  capital-value.  This  factor  is  for  the  present 
excluded  from  consideration. 

As  the  date  for  the  termination  of  the  annuity  approaches, 
the  total  discount  diminishes;  hence,  the  capital- value  of 
the  terminable  annuity  diminishes.  The  decrease  of  capi- 
tal-value is  what  is  sometimes  known  as  "wear  and  tear"; 
namely,  the  depreciation  of  an  article  due  to  the  fact  that  the 
services  left  for  it  to  render  gradually  diminish.  The  ap- 
proaching cessation  of  services  may  or  may  not  be  due  to 
physical  wear,  so  that  the  expression  "wear  and  tear"  is  a 

1  For  a  mathematical  presentation  of  this  proposition,  .see  Appen- 
dix to  Chap.  XIII,  §§  0,  7. 


SEC.  G]  VALUK    OF   CAPITAL  211 

misnomer.  We  can  imagine  an  article  which  suffers  no 
material  change,  and  of  which  the  services  will  nevertheless 
last  only  a  limited  period.  On  the  Atlantic  coast  the  fish- 
ermen sometimes  construct  temporary  platforms  which 
are  pretty  sure  to  disappear  in  the  September  gales.  It 
is  evident  that  the  value  of  such  a  property  will  decrease 
rapidly  as  the  end  of  the  fishing  season  approaches,  without 
this  decrease  being  due  in  the  least  to  any  physical  deteriora- 
tion. The  " World's  Fair"  buildings  at  St.  Louis  depre- 
ciated, during  the  brief  period  of  the  fair,  from  $15,000,000, 
which  was  first  paid  for  their  construction,  to  $386,000,  for 
which  they  were  sold  after  they  had  served  the  purpose  for 
which  they  were  built.  In  like  manner,  a  small  wooden 
bridge,  which  is  to  be  supplanted  by  a  larger  and  better 
structure  near  by,  will  decrease  in  value  rapidly  as  the  time 
approaches  for  the  other  structure  to  divert  its  traffic, 
without  any  corresponding  physical  deterioration.  Exam- 
ples are  common  enough  of  productive  instruments  losing 
their  value,  because  of  its  being  known  that  better  devices 
are  soon  to  displace  them.  "Wear  and  tear,"  therefore,  is 
a  phrase  which  we  must  use  only  in  a  metaphorical  sense. 
Even  when  the  wear  and  tear  take  place  because  of  physi- 
cal deterioration,  this  deterioration  acts  upon  the  value  only 
in  so  far  as  it  decreases  or  terminates  the  flow  of  income, 
and  not  because  of  a  physical  change  in  the  capital  which 
bears  this  income.1  The  value  of  the  capital  depends  ex- 
clusively on  the  income  from  it,  and  not  directly  upon  its 
physical  condition. 

§7 

Having  considered  the  case  of  a  terminable  annuity,  we 
turn  to  the  case  of  a  bond,  which  entitles  the  holder 
not  only  to  a  terminable  annuity,  but  also  to  a  single  de- 
ferred sum  culled  the  "  principal."  Thus,  a  so-called  "  five 

1  Cf.  Bohm-Buwerk,  Positive  Theory  of  Capital,  English  translation, 
1S91,  p.  347. 


212  NATURE    OF   CAPITAL   AND    INCOME      [CHAP.  XIII 

per  cent,  ten-year,  $100  bond"  means  the  right  to  receive 
an  annuity  of  $5  a  year  for  ten  years,  and,  in  addition, 
$100  at  the  end  of  the  ten  years. 

If  the  rate  of  interest  is  five  per  cent,  and  one  buys  a  bond 
which  entitles  him  to  an  annual  income  of  $5  a  year  for  ten 
years  and  $100  returnable  at  the  end  of  this  period,  it  is 
evident  that  the  purchase  price  of  the  bond  must  be  $100. 
In  this  case  the  $5  of  annual  income  is  the  interest  on  the 
purchase  price,  and  the  sum  of  $100  which  is  to  be  received 
at  maturity  is  equal  to  the  originally  invested  capital  or 
"principal."  For  these  reasons  such  a  bond  is  called  a  five 
per  cent  bond,  the  annual  installments  of  income  are  called 
"  interest,"  and  the  final  payment  of  $100  is  called  "  prin- 
cipal." 

But  more  often  than  not  the  bond  is  not  sold  at  par ;  con- 
sequently all  of  the  three  terms  just  mentioned  are  mis- 
nomers. If  the  bond  is  sold  above  par  the  rate  of  interest 
is  not  five  per  cent,  but  less  than  five  per  cent,  so  that  it  is 
only  nominally  a  "five  per  cent  bond";  the  $5  annually 
received  is  only  nominally  "interest";  and  the  $100  re- 
turnable at  the  end  is  only  nominally  "principal." 

In  order  to  obtain  the  capital-value  of  a  so-called  five 
per  cent  bond  when  the  market  rate  of  interest  is  four  per 
cent  (i.e.  when  the  bond  is  sold  on  a  four  per  cent  basis), 
we  need  simply  to  add  together  the  present  values  (reckoned 
at  four  per  cent)  of  the  ten  payments  of  $5  and  of  the  final 
payment  of  $100.  We  may  consider  these  items  as  consist- 
ing of  (1)  a  ten-year  annuity  of  $5  a  year,  and  (2)  a  sum  of 
$100  deferred  ten  years.  Both  of  these  we  can  easily  find 
from  the  explanations  already  given. 

It  has  been  explained1  that  the  present  value  of  a  ten- 
year  annuity  is  the  "total  discount"  on  the  capitalize,! 
value  of  a  corresponding  perpetual  annuity  beginning  when 
the  terminable  annuity  ceases.  Now  a  perpetual  annuity 
of  $5  is  worth,  if  interest  is  four  per  cent,  ^,  or  $125.- 

1  See  §  5,  supra.  2  Sec  §  3,  supra. 


SKC.  7]  VALUK   OF   CAPITAL  213 

A  perpetual  annuity  beginning  in  ton  years  will  thus  be 
worth  $125 — in  ten  year*.  To-day,  therefore,  it  is  worth, 
by  discounting  at  four  per  cent,  ^]lti>  or  $84.45.  The 
"total  discount"  is,  therefore,  $125  less  $84.45,  or  $40.55. 
We  need  to  add  to  this  the  other  element  in  the  bond, 
namely,  the  present  value  of  the  so-called  "principal"  of 
$100  due  in  ten  years.  Discounted  at  four  per  cent,  this 
is  worth  ^tiw»  or  $67.56.  Combining  our  two  figures  we 
have,  for  the  value  of  the  bond,  $40.55  +  $07.56,  or  S108.ll. 

We  find,  therefore,  that  a  so-called  five  per  cent  bond 
yields  the  investor  four  per  cent  if  it  is  bought  at  $108^^. 
In  like  manner  it  could  be  shown  that  it  will  yield  him  six 
per  cent,  if  bought  at  S92.50.1 

In  general  a  bond  sells  at  par  when  the  annual  income, 
or  nominal  "interest,"  is  equal  to  the  true  interest  on  the 
principal ;  it  sells  above  par  if  the  annual  income  (nominal 
interest)  is  greater  than  the  interest  on  the  principal ;  and 
below  par  if  it  is  less. 

In  a  similar  way  we  may  calculate  the  value  of  a  bond  in 
cases  where  the  installments  of  income,  or  nominal  interest, 
are  semi-annual  and  the  rate  of  interest  is  reckoned  semi- 
annually,  and  in  the  case  of  more  frequent  intervals,  as  well 
as  in  the  limiting  case  of  continuous  payment.2 

Elaborate  tables  have  been  constructed,  called  "bond 
value  books,"  calculated  on  the  foregoing  principles,  which 
are  used  by  brokers  for  showing  the  value  of  bonds  under 
different  circumstances.  The  tables  are  usually  employed, 
however,  for  the  converse  problem,  to  find  the  rate  of  in- 
terest "realized"  when  a  bond  is  bought  at  a  given  price. 
The  following  is  an  abridgment  of  these  tables,  for  (so- 
called)  three  per  cent,  four  per  cent,  and  five  per  cent  bonds. 
The  prices  of  the  bonds  in  all  cases  are  the  prices  taken 

1  For   a   mathematical  statement,   see  Appendix  to   Chap.   XIII. 
§  8;   for   an   alternative  method  of   calculating   the  value  of   a  bond 
and  one  which  gives  the   "premium"  separately,  see  Appendix   to 
Chap.  XIII,  §  9. 

2  For  mathematical  statement,  see  Appendix  to  Chap.  XIII,  §  10. 


214 


NATURE    OF   CAPITAL   AND   INCOME      [CHAP.  XIII 


RATES  OF  INTEREST 

(reckoned  semi-annually)  realized  on  a  bond  (with  semi-annual  cou- 
pons) known  as  a 

"  Three  per  cent  bond  " 


PRICE 

YEAKS  TO  MATURITY 

1 

2 

* 

K 

10 

20 

30 

50 

120 

1.8 

2.1 

2.3 

110 

1.9 

2.4 

2.5 

2.6 

105 

1.3 

2.0 

2.4 

2.7 

2.8 

2.8 

103 

1.5 

2.0 

2.4 

2.7 

2.8 

2.9 

2.9 

102 

2.0 

2.3 

2.6 

2.8 

2.9 

2.9 

2.9 

101 

2.0 

2.5 

2.7 

2.8 

2.9 

2.9 

2.9 

3.0 

100 

3.0 

3.0 

3.0 

3.0 

3.0 

3.0 

3.0 

3.0 

99 

4.0 

3.5 

3.4 

3.2 

3.1 

3.1 

3.1 

3.0 

98 

5.1 

4.1 

3.7 

3.4 

3.2 

3.1 

3.1 

3.1 

97 

6.1 

4.6 

4.1 

3.7 

3.4 

3.2 

3.2 

3.1 

95 

8.3 

5.7 

4.8 

4.1 

3.6 

3.3 

3.3 

3  2 

90 

8.6 

6.7 

5.3 

4.2 

3.7 

3.6 

3.4 

80 

7.9 

5.7 

4.5 

4.2 

3.9 

70 

7.3 

5.5 

4.9 

4.5 

Ditto  for  a  "Four  per  cent  bond 


YEARS  TO  MATURITY 


1  KlUf, 

1 

3 

3 

5 

10 

20 

3O 

5O 

130 

2.2 

2.6 

2.9 

120 

1.8 

2.7 

3.0 

3  '' 

110 

1.9 

2.8 

3.3 

3.5 

3.  (5 

105 

1.5 

2.3 

2.9 

3.4  \  3.7 

3.7 

3.8 

103 

2.5 

3.0 

3.3 

3.6 

3.S 

3.8 

3.9 

102 

2.0 

3.0 

3.3 

3.6 

3.8 

3.9 

3.9 

3.9 

101 

3.0 

3.5 

3.6 

3.8 

3.9 

3.9 

3.9 

4.0 

100 

4.0 

4.0 

4.0 

4.0 

4.0 

4.0 

4.0    4.0 

99 

5.0 

4.5 

4,4 

4.2 

4.1 

4.1 

4A 

4.1 

98 

0.1 

5.1 

4.7 

4.5 

4.3 

4.2 

4.1     4.1 

97 

7.2 

5.6 

5.1 

4.7 

4.4 

4.2 

4.2 

4.1 

95 

9.4 

6.7 

5.8 

5.2 

4.6 

4.4 

4.3    4.2 

90 

9.6 

7.8 

6.4 

5.3 

•1,8 

4.6 

4.5 

SO 

9.1 

6.8 

5.7 

5.6 

5.1 

SEC.  7] 


VALUF.    OF    CAPITAL 


215 


RATKS  OF  INYKHKST 

(reckoned  somi-annually)  realized  on  a  bond  (with  semi-annual  cou- 
pons) known  as  a 

''  I1' in-  /:cr  n  nl  liun/l  " 


VI:AI:S  n>  MATI  UITY 


1  I  „!  1 

1 

« 

3 

.-, 

IO 

20 

.•50 

r>o 

140 

2.5 

3.0 

3.4 

130 

1  .7 

3.0 

3.4 

3.7 

120 

2.7 

3,6 

3.9 

4.1 

110 

1.6 

2.8 

3.8 

4.3 

4.4 

4.5 

105 

2.4 

3.2 

3.9 

4.4 

4.6 

4.7 

4.7 

103 

2.0 

3.4 

3.9 

4.3 

4.6 

4.8 

4.8 

4.8 

102 

3.0 

4.0 

4.3 

4.6 

4.8 

4.8 

4.9 

4.9 

101 

4.0 

4.5 

4.6 

4.8 

4.9 

4.9 

4.9 

5.0 

100 

5.0 

5.0 

5.0 

5.0 

5.0 

5.0 

5.0 

5.0 

99 

6.1 

5.5 

5.4 

-  •> 

5.1 

5.1 

5.1 

5.1 

98 

7.1 

6.1 

5.7 

5.5 

5.3 

5.2 

5.1 

5.1 

97 

8.2 

6.6 

G.I 

5.7 

5.4 

5.2 

5.2 

5.2 

95 

7.7 

6.9 

(  .2 

5.7 

5.4 

5.3 

5.3 

90 

8.9 

.  .4 

6.4 

5.9 

5.7 

5.6 

80 

7.9 

6.9 

6.5 

6.3 

immediately  after  an  installment  of  income.  They  are 
what  business  men  call  "ex-interest"  prices,  i.e.  are  devoid 
of  accrued  interest.  To  use  the  tables  when  we  have  given 
the  price  at  any  time  between  two  installments  of  income, 
it  is  necessary  first  to  "strip"  this  price  of  the  interest 
accrued  since  the  last  installment  of  income. 

It  may  be  asked,  Where  is  the  line  of  demarcation  be- 
tween what  are  nominally  "principal"  and  "interest"? 
The  answer  is :  None  at  all  of  any  logical  importance. 
In  our  calculations  all  the  items  receivable  from  the  bond, 
including  the  principal  when  paid,  have  been  treated  on 
the  same  basis.  They  are,  with  respect  to  the  bond,  its 
true  "income."  The  so-called  "principal"  is  usually  re- 
garded as  a  repayment  of  the  original  investment.  Ap- 
proximately, the  original  investment  and  final  "principal" 
are  equal.  But  whether  equal  or  not  they  are  distinct. 


216  NATURE    OF    CAPITAL   AND    INCOME       [CiiAP.  XIII 

The  original  investment  is  the  discounted  value  of  expected 
receipts;  the  final  "returned"  principal  is  simply  one  (the 
largest  one)  of  those  receipts.  The  only  difference  between 
this  large  receipt  and  the  other  smaller  ones  is  that,  usually, 
it  is  employed  differently  when  received.  It  is  usually 
reinvested  in  other  long-time  securities,  whereas  the  smaller 
items  of  income,  the  so-called  "interest,"  are  spent  for  arti- 
cles of  shorter  duration,  and,  thereby,  soon  converted 
into  true  "final  income."  The  "principal"  and  "interest," 
therefore,  while  both  are  income  with  reference  to  the  bond 
considered  by  itself,  are  apt  to  lead  to  different  results  when 
followed  into  the  final  transformations  of  purchase  and 
sale,  by  the  debit  and  credit  cancellations  previously  ex- 
pounded. If  we  suppose  a  five  per  cent  bond  to  be  always 
sold  on  a  five  per  cent  basis,  and  the  principal  to  be  always 
reinvested  in  the  same  kind  of  security,  it  is  evident,  in 
relation  to  the  whole  series  of  operations,  including  the  rein- 
vestment, that  the  principal,  though  income,  is  immediately 
canceled  by  reinvestment  as  outgo.  In  other  words, 
whenever  it  appears  as  income  from  one  bond,  it 
immediately  disappears  again  as  outgo  for  another;  con- 
sequently the  owner  is  virtually  in  possession  of  a  per- 
petual annuity  of  So  a  year.  It  is  with  a  view  to  such  an 
operation  that  the  final  payment  of  $100  on  a  bond  is  in- 
stinctively regarded  on  a  different  footing  from  the  other 
payments  called  "  interest."  It  is  called  "  principal  "  on 
the  theory  that  it  is  to  be  reinvested  in  order  to  continue 
the  annuity  of  $5.  It  thus  in  theory  represents  capital, 
whereas  the  other  payments  represent  only  income.  But 
we  see  now  that  both  are  income  received  from  the  bond 
as  a  source  of  income,  although  either  may,  by  reinvestment, 
be  put  into  capital.  That  one  of  them  is  usually  put  back 
into  capital  and  the  other  not,  is  a  matter  of  subsequent 
history  and  does  not  affect  the  immediate  study  of  the 
bond  itself. 

Kven  when  the  "principal"  received  at  the  maturity  of 


SEC.  8]  VALUK    OF   CAPITAL  217 

the  bond  is  reinvested,  it  may  be  that  it  is  not  equal  to 
the  original  investment,  nor,  therefore,  to  the  capital-value 
of  the  bond  at  any  time  before  maturity.  This  equality 
would  hold  true  only  in  case  the  bond  is  always  kept  at 
par.  When  it  is  worth  more  or  less  than  par  the  capital- 
value  is  more  or  less  than  the  "principal,"  and  for  this 
reason,  if  for  no  other,  the  capital-value  should  not  be 
confounded  with  the  ''  principal." 

In  order  to  determine  whether  or  not  a  nominally  five 
per  cent  bond  really  yields  five  per  cent,  we  must  refer  to 
the  price  at  wrhich  it  sells,  and  while  there  is  no  neces- 
sity to  abandon  the  terminology  by  which  "principal" 
and  "interest"  are  used  with  reference  to  bonds,  these 
terms  are  undoubtedly  misnomers  and  their  existence  is 
responsible  for  considerable  confusion.  For  instance, 
insurance  companies  have  recently  been  offering  their 
policy  holders  an  option  between  the  receipt  at  the  death 
of  the  insured  of  a  definite  insurance  of  SI 300,  or  of  a 
"five  per  cent  gold  bond"  for  $1000.  The  gold  bond  has 
seemed,  to  many  policy  holders,  a  tempting  form  of  invest- 
ment because  of  the  "  high  rate  of  interest,"  —  five  per  cent ; 
but  it  is  evident  that  such  a  bond,  considered  as  the  equiva- 
lent of  $1300  in  cash,  is  on  a  lower  basis  than  five  per  cent. 


Hitherto  we  have  considered  only  four  special  cases  of 
capitalizing  income,  viz.  (1)  the  capital-value  of  a  single 
income  item ;  (2)  the  capital- value  of  a  perpetual  annuity ; 
(3)  the  capital-value  of  an  annuity  terminable  in  a  definite 
number  of  years;  and  (4)  the  capital- value  of  a  bond.  But 
it  is  clear  that  the  items  of  income  from  any  property  may 
occur  in  many  other  forms,  may  last  for  any  length  of  time, 
and  may  be  distributed  through  this  time  in  any  manner 
whatever.  Let  us,  therefore,  consider  the  general  case  in 
which  any  random  series  of  income  items,  AB,  A'B' ,  A"B", 
Ar"B'" ',  are  received,  as  shown  in  Figure  4.  The  capital- 


218 


NATURE    OF    CAPITAL   AND    INCOME       [CHAP.  XIII 


value  of  this  series  at  the  point  of  time  0  is  found  by 
adding  together  the  present  value  of  the  separate  items. 
The  best  way  to  exhibit  this  is  to  begin  at  the  last  income 

J  O 

payment,  A'"B"' .  Just  after  this  last  installment,  of 
course,  the  property  is  valueless;  that  is,  its  capital-value  is 
zero.  Just  before  this  installment  the  capital-value  is  equal 
to  the  installment  itself,  and  is  represented  by  A'"B"r ,  At 

D 


FIG.  4. 

any  time  in  the  interval  between  this  installment  of  income 
and  the  next  preceding  installment,  the  value  will  evidently 
be  found  by  following  the  discount  curve  B'"C" ,  C"  being 
vertically  over  A".  The  height  A"C"  is,  therefore,  the 
capital- value  of  the  property  just  after  the  payment  A"B" . 
Its  capital-value  just  before  this  payment  is  found  by  adding 
the  vertical  line  C"D",  equal  to  the  installment  of  income 
A"B" .  From  D"  in  turn  we  proceed  backward  along  the 
discount  curve  D"C'to  C',  at  which  point  A'C'  represents  the 
capital-value  of  the  property  just  after  the  installment  A'B' . 
To  this  is  added,  if  we  pass  back  an  instant,  an  amount 
C'\y  equal  to  the  installment  A'B' .  The  result  is  A'//, 
the  capital-value  just  before  said  installment.  From  D',  in 


Sue.  8] 


VALUK    OF    CAPITAL 


219 


turn,  the  capital-value  descends  along  the  discount  curve 
to  C,  where  CD,  equal  to  AB,  is  added,  and  from  I)  wo 
proceed  finally  by  discount  curve  to  P,  vertically  over  0. 
OP  is,  therefore,  the  capital-value  of  the  property  at  the 
"present  "  instant,  and  its  value  at  any  succeeding  in- 
stant is  shown  by  following  the  course  of  the  broken  line 
PDCD'CfD"C"Bf"Af".1  This  curve  must  descend  to  zero 

D' 


B1 


B 
FIG.  5. 

finally,  when  the  income  is  exhausted,  and  it  usually 
shows  a  tendency  to  decrease  before  this  last  payment 
is  reached. 

If,  in  a  series  of  income  items,  a  negative  one  occurs,  it  is 
only  necessary  to  reverse  the  capital  curve,  as  shown  in 
Figure  5,  where  the  first  installment,  AB,  is  outgo  instead 
of  income.  The  curve  PB"  evidently  represents  the  be- 
havior of  capital-value,  rising  suddenly  as  the  outgo  AB 
is  passed  and  falling  when  the  income  A'B'  is  received, 
and  so  on  to  the  end. 

We  may,  if  we  choose,  trace  the  history  of  the  value  of  a 
security  from  the  time  immediately  before  its  purchase,  and 
consider  the  purchase  price  itself  as  an  outgo.  If  this  price 


1  For  the  mathematical  formula  for  the  capital-value  of  any  series 
of  income  installments,  see  Appendix  to  Chap.  XIII,  §  11. 


220 


NATURE   OF   CAPITAL   AND   INCOME      [CuAP.  XIII 


is  exactly  equal  to  the  discounted  value  of  the  succeeding 
income,  it  is  evident  that  the  value  immediately  before  its 
purchase  must  be  exactly  zero.  Thus  in  Figure  6  let  OM 
be  the  purchase  price,  and  equal  to  OA,  which  is  the  capital- 
value  immediately  after  purchase.  The  capital-value 
immediately  before  purchase  is,  therefore,  zero,  and  the 
entire  capital  curve  is  the  line  OABCDEFH,  which  starts 


FIG.  6. 

at  zero  and  ends  at  zero,  but  is  above  the  zero  line  at  all 
intermediate  intervals.  This  represents  the  normal  his- 
tory of  any  capital  instrument  if  bought  at  a  "  fair 
price." 

If  the  flow  of  income  is  continuous,  we  may  obtain  the 
capital-value  approximately   by  dividing  the   continuous 


SEC.  0]  VALUi:    OF    CAPITAL  221 

income  stream  into  arbitrary  installment  sand  discounting 
each  installment  separately.1 

The  value  of  the  income  stream  has  heretofore  been 
always  reckoned  in  advance1  of  its  occurrence;  that  is,  we 
have  discounted  income  to  obtain  jirevcnt  value.  We  may, 
however,  consider  an  income  as  paid  for  at  the  close  of 
the  period,  in  which  case  we  have  to  deal  with  its  "accu- 
mulated" value  or  its  "amount." 

§0 

Thus  far  we  have  considered  the  possibility  of  but  one 
income  stream  from  any  given  capital  wealth.  But  it  often 
happens  that,  with  one  capital  instrument,  there  is  a  choice 
between  various  income  streams.  Land  may  be  used  for 
grazing,  agriculture,  building,  or  recreation  purposes. 
Tools  may  be  employed  in  a  variety  of  ways,  and  the  same 
is  true  of  innumerable  articles  of  wealth,  particularly  when 
taken  in  combination.  What  determines  the  choice  of  the 
series  of  uses  to  which  any  given  instrument  may  be  put? 
Evidently  that  series  of  uses  or  income  stream  will  be  se- 
lected which  yields  the  maximum  present  value.  Thus, 
if  land  used  for  grazing  purposes  will  yield  a  net  service  of 
81000  a  year  forever,  and  interest  is  taken  at  four  per  cent, 
its  value  for  grazing  purposes  is  evidently  825,000.  If, 
in  like  manner,  the  capital-value  for  some  other  use,  say  for 
growing  wheat,  is  $20,000,  it  is  clear  that  the  land  will  be 
employed  for  grazing  rather  than  for  growing  wheat. 

Sometimes  the  two  series  of  uses  to  which  land  or  other 
wealth  may  be  put  differ,  not  only  in  their  amount,  but  in 
their  time  of  beginning  or  ending.  In  a  city,  for  instance, 
land  may  be  used  either  for  present  dwelling  or  for  future 
business-purposes,  and  it  often  becomes  a  question  which 
use  is  the  more  valuable.  In  case  the  city  is  growing 

1  For  a  fuller  statement,  see  Appendix  to  Chap.  XIII,  §  12. 

2  For  discussion,  and  for  formuhe  for  the  capital-value  of  any  in- 
come, discontinuous  or  continuous,  see  Appendix  to  Chap.  XIII,  §  13. 


222  NATURE   OF   CAPITAL   AND   INCOME      [CHAP.  XIII 

rapidly,  it  may  happen  that  in  certain  quarters,  although 
the  present  use  for  dwelling  purposes  is  more  important,  in 
a  few  years  the  locality  will  cease  to  be  a  residence  quarter 
and  the  land  will  be  needed  for  business  purposes.  In  such 
cases,  it  may  "pay  "  to  keep  the  land  out  of  present  use  en- 
tirely and  reserve  it  until  the  city  has  grown  so  as  to  make 
it  profitable  to  erect  a  business  block.  If  the  land  were  now 
encumbered  with  a  dwelling,  either  the  possibility  of  its 
subsequent  use  for  business  purposes  would  be  cut  off, 
or  the  profit  from  its  conversion  to  those  purposes  would  be 
impaired  by  the  prior  destruction  and  waste  of  the  dwelling. 
Under  such  circumstances  it  would  usually  happen  that 
speculators  would  buy  up  and  hold  the  land.  The  manner 
in  which  the  gain  presents  itself  to  them  is  simply  as  a  pro- 
spective rise  in  value  from  the  growth  of  the  city;  they 
therefore  buy  the  land  to  sell  it  later  at  a  higher  price. 
Such  a  speculator  is  commonly  regarded  as  keeping  land 
"out  of  use."  He  is,  however,  only  deferring  the  use,  and, 
if  he  has  foresight,  is  no  more  to  be  condemned  than  the 
wise  speculator  on  the  wrheat  exchange,  whose  work,  as  is 
well  known,  operates  to  conserve  the  supply  of  wheat.  The 
speculator  thus  tends  to  bring  about  the  best  utilization  of 
the  land  in  the  sense  that,  out  of  several  alternative  income 
streams  which  the  land  might  be  made  to  yield,  that  one  is 
selected  which  possesses  for  him  the  maximum  present 
value.  In  general  it  is  probable  that  the  best  uses  of  the  land 
for  the  public  also  are  found  in  this  way.  The  latter  con- 
clusion does  not,  however,  absolutely  follow  from  the  former, 
since  the  "  best "  uses  are  not  necessarily  those  which 
have  the  greatest  market  value;  but  those  who  would 
prevent  all  land  speculation  will  at  least  need  to  adduce 
other  arguments  than  that  speculation  "  keeps  land  out  of 
use,"  before  they  have  proven  their  case;  for  wise  land 
speculation  means  simply  the  discriminating  choice,  out  of  a 
number  of  uses,  of  that  use  or  series  of  uses  which  affords 
to-day  the  greatest  present  value. 


SEC.  10]  VALUE    OF   CAPITAL  223 

It  should  be  observed  that  if  the  rate  of  interest  is  raised, 
the  relative  advantages  of  the  two  uses  in  the  example 
given  might  be  quite  different.  In  this  ease  it  might  pay 
to  put  up  the  dwelling  rather  than  wait  for  the  business 
block;  for  the  holder  of  the  land,  as  he  expresses  it,  could 
not  afford  to  "lose  his  interest"  when  it  is  at  so  high  a  rate. 

§  10 

Thus  far  we  have  considered  the  capital-value  only  of 
individual  articles  of  wealth.  The  same  reasoning  applies 
to  a  group  of  articles  of  wealth.  An  important  case  is 
that  of  a  merchant's  stock.  In  this  case  we  may  prefer 
to  capitalize  the  stock  as  a  whole  rather  than  to  take 
the  sum  of  the  capitalizations  of  its  separate  elements. 
The  net  income  from  the  stock  is  found  by  subtracting 
from  the  gross  income  all  the  outgo,  including,  besides 
the  cost  of  replenishing  the  stock,  the  other  costs  of  the 
business,  — clerk  hire,  rent,  and  even  an  allowance  for  the 
work  of  the  merchant  himself,  unless  he  is  a  mere  "silent 
partner."  If  the  net  income  is  supposed  to  remain  constant 
forever,  the  capital  value  of  the  stock  will,  of  course,  be 
found  by  dividing  the  net  income  by  the  rate  of  interest. 
In  this  case  the  rate  of  interest  must  be  taken  for  the  proper 
installment  interval.  If  the  goods  are  supposed  to  be  con- 
tinuously bought  and  sold,  the  rate  to  be  employed  is  the 
"rate  of  interest  per  annum  reckoned  continuously."  * 

§11 

We  conclude,  therefore,  that  the  value  of  any  capital- 
good,  either  of  wealth  or  of  property-rights,  assuming  that 
all  future  income  is  foreknown,  is  the  discounted  value  of 
that  income,  and  consequently  that,  as  time  goes  on,  the 
value  of  that  capital  will  oscillate,  rising  gradually  during 
intervals  between  installments  along  a  "discount  curve," 


224  NATURE    OF    CAPITAL   AND    INCOME      [CHAP.  XIII 

as  the  future  income  approaches,  and  falling  suddenly  as  the 
installments  are  successively  passed  by  and  acting  in  a 
contrary  manner  before  and  after  an  outgo.  This  os- 
cillation of  c'apital-value  ends  finally  at  zero,  when  the 
life  or  service  of  the  article  or  group  is  ended.  It  also  often 
begins  at  zero,  when  the  instrument  or  group  is  one  that  is 
newly  acquired  or  produced.  These  changes  constitute, 
as  it  were,  a  sort  of  life  history  of  capital- value.1 

It  may  seem  to  some  readers  that  there  is  an  exception 
to  the  rule  that  the  value  of  capital  is  the  discounted 
value  of  its  expected  income,  in  the  case  where  the 
income  which  might  be  received  from  the  capital  is  in- 
definitely postponed.  This  is  the  case  in  which  the  "prin- 
cipal" accumulates  at  compound  interest  so  that  no  "  in- 
terest" is  withdrawn.  If  a  person  has  a  deposit  of  $1000 
in  a  savings  bank  and  leaves  it  there  to  accumulate  at  4 
per  cent  until  it  amounts  to  double  that  sum,  which  will 
happen  in  about  eighteen  years,  the  $1000  does  not  appear 
to  him  to  be  the  discounted  value  of  any  income.  If  he 
thinks  of  it  as  the  discounted  value  of  anything  at  all,  it 
will  be  of  the  $2000  of  capital  which  he  expects  to  own  at 
the  end  of  eighteen  years.  It  is  perfectly  true  that  the 
capital-value  of  $1000  is  the  discounted  value  of  the  future 
capital-value  of  $2000;  but  the  latter  capital-value  is 
itself  the  discounted  value  either  of  some  subsequent 
income,  or,  in  turn,  of  a  capital  still  further  deferred,  and 
so  on  indefinitely.  Actual  income  is  hoped  for  some- 
time, even  if  it  be  not  for  a  million  years.  The  present 
$1000  is  the  discounted  value  of  that  ultimate  income,  how- 
ever far  distant.  A  perpetual  accumulation  is,  humanly 
speaking,  out  of  the  question.  But  if  such  perpetual 
accumulation  be  regarded  for  the  moment  as  possible,  it 
may  still  be  interpreted  as  a  perpetual  postponement  of 
possible  income;  so  that  even  in  this  case  the  $1000  may 

1  For  mention  of  the  case  where  the  rate  of  interest  changes  and  its 
changes  are  foreknown,  see  Appendix  to  Chap.  XIII,  §  15. 


SEC.  11]  VALUE    OF    CAPITAL  225 

still  be  regarded  as  the  discounted  value  of  an  income 
which  is  indefinitely  postponed,  but  indefinitely  great.  Of 
course,  such  a  limiting  case  is  of  purely  theoretical  interest. 
The  prodigious  sums  which  result  from  the  reckoning  of 
compound  interest  always  surprise  those  who  have  never 
made  such  computations.  One  dollar  put  at  compound 
interest  at  4  per  cent  would  amount,  in  one  century,  to 
$50,  in  a  second  century  to  $2500,  in  a  third  century 
to  $125,000,  in  a  fourth  century  to  $6,5(K),()(K),  in  a 
fifth  century  to  $325,000,000,  and"  in  a  sixth  century  to 
$16,000,000,000.  Beyond  this  the  figures  are  almost 
unthinkable  in  magnitude.1 

Yet  we  have  few  instances  in  which  any  one  has  endeav- 
ored to  set  aside  even  one  dollar  for  the  benefit  of  posterity 
six  centuries  removed !  There  is  too  much  reluctance  to 
build  for  the  remote  future,  even  though  the  attainable 
results  are  enormous.  Benjamin  Franklin,  at  his  death 
in  1790,  left  £1000  to  the  town  of  Boston  and  the  same  sum 
to  Philadelphia,  with  the  proviso  that  it  should  accumulate 
for  a  hundred  years,  at  the  end  of  which  time  he  calculated 
that  at  5  per  cent  it  would  amount  to  £131,000.  In  the 
case  of  the  Boston  gift,  it  actually  amounted,  at  the  end 
of  the  century,  to  $400,000,  and  has  since  accumulated  to 
about  $600,000.  The  sum  received  by  the  city  of  Phila- 
delphia has  not  increased  nearly  as  fast. 

Another  interesting  case  of  accumulation  is  that  of  the 
Lowell  Institute  in  Boston,  which  was  founded  by  a  bequest 
of  $200,000  in  1838,  with  the  condition  that  10  per  cent  of 
the  income  from  it  should  be  reinvested  and  added  to  the 
principal.  The  peculiarity  of  this  provision  is  that  it 
applies  in  perpetuity.  There  is,  therefore,  theoretically  no 
limit  to  the  future  accumulation  thus  made  possible. 
The  fund,  after  sixty-seven  years,  amounts  already  to 
$1,100,000. 

It  must  be  remembered  however  that  practically  even  a 

1  For  a  geometrical  representation,  see  Appendix  to  Chap.  XIII,  §  16. 
Q 


226  NATURE    OF    CAPITAL   AND    INCOMIO      [CHAP.  XIII 

small  sum,  such  as  $1000,  if  allowed  to  accumulate,  let  us 
say,  at  4  per  cent  for  1000  years,  could  never  actually 
attain  the  theoretical  magnitude.  This  is  evident  from 
the  fact  that  the  theoretical  sum  would  then  amount  to 
over  $100,000,000,000,000,000,  which  is  so  far  in  excess  of 
the  total  value  of  capital  on  this  planet,  as  to  be  out  of 
the  range  of  possibility.  The  reason  the  sum  would  fail 
to  accumulate  as  fast  as  theoretically  required,  aside  from 
fortuitous  losses,  lies  in  the  reduction  of  the  rate  of  in- 
terest which  the  very  accumulation  would  bring  about. 
The  administrators  of  such  a  fund,  as  the  centuries  passed 
by,  would  find  it  increasingly  difficult  to  obtain  fields  in 
which  to  invest  it,  and  their  effort  so  to  invest  would  have 
the  same  effect  in  reducing  the  rate  of  interest  realized  on 
the  investments  as  is  now  felt  by  the  national  banks  in 
their  pressure  to  buy  government  bonds. 


CHAPTER  XIV 


EARNINGS   AND    INCOME 


IN  the  last  chapter  it  was  shown  that,  perfect  foresight 
being  assumed,  the  value  of  any  capital  good  is  derived  from 
its  future  income  by  discounting  the  value  of  that  income. 
It  now  remains  to  compare  the  capital-value  thus  derived 
with  the  expected  income-value  on  which  it  depends. 

It  is  evident  at  the  outset  that  the  capital-value  is  less 
than  the  total  expected  income;  for  the  discounted  value 
of  any  future  sum  is  necessarily  less  than  that  sum  itself. 
This  fact  is  illustrated  in  the  third  and  fourth  columns  of 
the  following  table  of  capital  and  income  in  the  cases  of 
five  typical  articles :  — 


CAPITAL 

NET  INCOME  PEK  YEAH 

TOTAL 
INCOME 

CAPITA  L- 

VAU'K    (INT. 

AT  5%) 

CAPITAL- 

VALTE    (1ST. 

AT   lij%) 

Land 

SI  000  per  year  for- 

ever     

Infinite 

820,000.00 

840,000.00 

House 

SI  000  per  year  for 

50  years  .... 

850,000.00 

18,300.00 

28,400.00 

Horse 

S100  per  3rear  for 

6  years    .... 

600.00 

508.00 

551.00 

Suit    of 

820  1st   year;    810 

clothes 

2d  year  .... 

30.00 

28.00 

29.00 

Loaf  of 

S36.50  per  year,  for 

bread 

1   day      .... 

.10 

.10 

.10 

In  this  table  we  observe  that  the  value  of  the  land,  when 
interest  is  at  5  per  cent,  is  820,000,  whereas  the  total  in- 
come to  be  expected  from  it  is  infinitely  greater;  that  the 


227 


228  NATURE   OF   CAPITAL   AND   INCOME       [CHAP.  XIV 

value  of  the  house  when  interest  is  at  the  same  rate  is 
SI 8,300,  whereas  the  total  income  to  be  expected  from  it  is 
about  three  times  as  much,  or  §50,000;  that  the  value  of 
the  horse  is  a  little  over  $500,  whereas  the  total  expected 
income  is  about  $100  more,  or  $600 ;  that  the  value  of  the 
suit  of  clothes  is  $28,  whereas  its  total  income  is  $30,  of 
which  $20  accrues  the  first  year  and  $10,  the  second;  and, 
finally,  that  the  capital-value  of  the  loaf  of  bread  is  10 
cents  and  the  income  expected  from  it  is  also  10  cents. 
In  this  limiting  case  there  is  practically  no  diminution  on 
account  of  the  interval  of  time  to  elapse  between  the  time 
of  valuing  the  instrument  and  the  time  of  receiving  its 
services,  for  the  reason  that  this  time  is  too  brief. 

From  the  table  we  see  clearly  one  reason  that  certain 
articles  have  been  identified  with  income  and  others 
not.  Bread  has  practically  the  same  capital-value  as 
income-value,  so  that,  if  a  person  were  not  accustomed  to 
fine  distinctions,  he  might  think  it  unnecessary  to  discrimi- 
nate between  the  10  cents  which  is  the  value  of  the  use  of 
the  bread,  and  which  is,  therefore,  income,  and  the  10  cents 
which  is  the  value  of  the  bread  itself,  and  which  is,  therefore, 
capital.  There  is  almost  as  much  danger  of  such  confusion 
in  the  case  of  clothing ;  for  there  is  only  a  slight  difference 
between  the  $30  which  is  the  value  of  the  use  of  the  suit, 
and  is  therefore  income,  and  the  $28  which  is  the  value  of 
the  suit,  and  is  therefore  capital.  But  as  we  pass  to  the 
more  enduring  articles,  there  emerges  so  wide  a  difference 
between  the  value  of  the  use  of  an  instrument  and  the  value 
of  the  instrument  itself,  that  there  is  no  difficulty  in  dis- 
tinguishing between  them.  Accordingly  we  usually  find  in 
treatises  on  economics  some  distinction  between  the  value 
of  the  use  of  a  house  ($50,000  in  the  foregoing  table)  and 
the  value  of  the  house  itself  ($18,300  in  the  table).  But  if 
the  distinction  is  valid  in  one  case  it  is  valid  in  the  others. 
The  consequence  of  disregarding  it  we  have  already  seen 
in  Chapter  VII. 


SEC.  2]  EARNINGS   AND    INCOME  229 

§2 

If  the  rate  of  interest  is  not  f>  per  cent,  but  2}2  per  cent, 
there  will  result  great  differences  in  the  capital-values. 
The  consequences  are  seen  in  the  last  column  of  the; 
table.  But  the  effect  on  capital-values  wrought  by  thus 
cutting  the  rate  of  interest  in  two  will  be  different  for  each 
of  the  five  different  articles.  The  more  enduring  ones  will 
be  affected  the  most.  When  the  rate  of  interest  is  halved 
the  value  of  the  land  will  be  doubled,  rising  from  $20,000  to 
$40,000,  but  the  value  of  the  house  will  rise  by  only  about 
60  per  cent,  i.e.  from  $18,300  to  $28,400;  the  value  of  the 
horse  will  rise  only  10  per  cent,  i.e.  from  $508  to  $551 ;  the 
value  of  the  suit  will  rise  only  from  $28  to  $29;  and,  finally, 
the  value  of  the  loaf  of  bread  will  not  rise  at  all,  but  will 
remain  at  10  cents.  We  see  in  these  five  types  of  articles 
that  the  sensitiveness  of  capital-value  to  a  change  in  the 
rate  of  interest  is  the  greater  the  more  enduring  the  income. 

In  general,  also,  this  sensitiveness  is  the  greater  the  more 
remote  the  periods  of  time  at  which  the  income  is  concen- 
trated. For  instance,  if  the  total  income  is  $100,  and  is 
all  concentrated  at  a  point  of  time  fifty  years  distant,  its 
capital-value,  when  the  rate  of  interest  is  5  per  cent,  is  $8.72, 
but  it  becomes  $29.09  when  the  rate  of  interest  is  reduced  to 
2-J-  per  cent.  That  is,  the  rate  of  interest  being  halved,  the 
capital-value  is  more  than  trebled.  If  the  same  income  of 
$100  were  to  be  due  only  one  year  from  date,  the  change 
from  5  per  cent  to  2.]  per  cent  in  the  rate  of  interest  would 
elevate  the  capital- value  only  from  $95  to  $97.50. 

§3 

Thus  far  we  have  been  concerned  only  with  total  income. 
in  relation  to  capital-value ;  we  now  consider  the  rate  of 
income  per  year  in  relation  to  capital-value.  This  ratio 
has  already  been  called  the  rate  of  "value-return." 

In  accordance  with  previous  explanations  the  sequence 


230  NATURE    OF    CAPITAL   AND    INCOME       [CHAP.  XIV 

of  calculating  the  rate  of  value-return  is  as  follows: 
A  specified  property  entitles  the  owner  to  a  future  series  of 
income  items  which  is  assumed  to  be  definitely  foreknown. 
These  items  are  all  discounted  by  means  of  a  specified  rate 
of  interest.  The  sum  of  the  discounted  values  constitutes 
the  capital-value  of  the  property.  This  capital-value,  at 
any  time,  taken  as  divisor  and  the  income  per  year  taken  as 
a  dividend  gives  the  rate  of  value-return  as  quotient. 

It  must  be  steadily  borne  in  mind  that  the  value  of  the 
capital  which  forms  the  divisor  is  not  a  fictitious  book 
value,  nor  the  value  as  indicated  by  the  sum  of  money 
originally  invested,  but  is  simply  the  discounted  value,  at 
the  specified  time,  of  the  expected  income  subsequent  to 
that  time.  We  should  at  the  outset  rid  our  minds  of 
the  bogey  of  an  unvarying  "principal"  perpetually  existing 
somewhere  in  a  debt  or  other  property.  The  only  value 
entity  we  have  to  deal  with  is  the  value  of  the  property 
considered,  which  is  the  discounted  value  of  the  expected 
income,  and  which  therefore  is  continually  changing. 
When  capital  is  for  the  present  yielding  no  income,  as, 
for  instance,  vacant  land,  it  nevertheless  is  expected  some- 
time to  yield  income,  and  it  is  the  discounted  value  of  this 
remote  income  which  alone  constitutes  the  present  value 
of  the  land.  It  is  true  that  a  speculator  may  prize  the 
land  simply  because  he  thinks  he  can  sell  it  later  to  some 
one  else,  and  to  him  it  may  seem  that  its  value  is  inde- 
pendent of  any  future  income,  and  depends  only  on  the 
future  capital-value  at  which  he  expects  to  sell.  But  it  is 
clear  that  this  future  capital- value  is  itself  the  discounted 
value  of  the  income  which  the  then  purchaser  will  expect. 
Or,  if  he  too  be  a  speculator,  and  his  valuation,  like  his 
predecessor's,  depends  on  a  resale,  the  dependence  on 
future  income  is  merely  again  postponed  to  the  time  when 
some  purchaser  shall  buy  the  land  for  the  income  it  will 
yield.  This  ultimate  expected  income  gives  the  basis  for 
all  prior  capital  valuations.  Were  there  no  expectation 


SEC.  4]  KARXIXGS    AND    INCOME  231 

of  any  future  income — -or,  at  least,  the  expectation  that 
there  would  be  an  expectation  of  it — -there  could  be  no 
capital-value.  Capital-value,  independent  of  expected  in- 
come, is  impossible. 

§4 

The  first  proposition  to  be  emphasized  as  to  the  rate  of 
value-return  is  that  it  is  not  necessarily  equal  to  the  rate  of 
interest,  but  may  be  either  greater  or  less  than  that  rate,  and 
to  any  degree. 

Let  us  take,  for  example,  the  case  of  the  house  which  we 
assumed  would  endure  just  fifty  years,  giving  throughout 
that  period  a  shelter-service  worth,  after  actual  expenses 
are  deducted,  $1000  annually.  We  saw  that  its  value, 
computed  by  discounting  this  fifty-year  annuity  on  a  5  per 
cent  basis,  is  $18,300.  It  therefore  yields  the  first  year  a 
rate  of  value-return  on  its  capital-value  of  ™^,  or  5.4  per 
cent.  At  the  end  of  ten  years  its  value,  found  by  dis- 
counting the  income  still  remaining,  will  be  SI 7, 200.  It 
will  therefore  then  be  yielding  a  value-return  of  ^'^  per 
year,  or  5.8  per  cent.  At  the  end  of  thirty  years,  in  like 
manner,  it  will  be  worth  $12,500  and  yielding  j™[|0,  or  8  per 
cent.  Again,  the  suit  of  clothes  which  will  last  two  years, 
and  gives  services  worth  $20  the  first  year  and  $10  the 
second,  has  a  value  at  the  start  of  about  $28,  and  at  the  end 
of  the  first  year  of  about  $9.50.  The  value-return  the  first 
year  is  therefore  j|,  or  71.4  per  cent,  and  the  second  year 
9-°-0,  or  over  100  per  cent.  The  loaf  of  bread  has  a  value 
of  10  cents.  It  yields  10  cents'  worth  of  income  in  a  day, 
which  is  at  the  rate  of  $36.50  per  year;  consequently  its 
value-return  is  —f^,  or  a  rate  of  36,500  per  cent  per  annum 
(interest  reckoned  daily  or  "continuously"). 

In  these  examples  the  value-return  exceeds  the  rate 
of  interest.  Reversely,  it  is  possible  for  the  value-return 
on  capital  to  be  less  than  the  rate  of  interest.  If,  for  in- 
stance, forest  land  with  small  trees  is  bought,  it  may  be 


232  NATURE    OF    CAPITAL    AND    INCOME       [CHAP.  XIV 

that  no  product  can  be  obtained  until  the  end  of  ten  years. 
We  may  suppose  that  then  the  yield  is  worth  $1000  a  year 
during  the  ensuing  (second)  decade,  after  which  it  will  be 
worth  $2000  a  year  forever.  It  may  be  shown  that  the 
present  value  of  the  forest,  reckoned  on  a  five  per  cent  basis, 
is  about  $20,000.  This  would  be  the  discounted  value  of  an 
annuity  of  $1000  a  year,  whose  commencement  is  deferred 
ten  years  from  the  date  of  investment,  and  which  then 
runs  ten  years,  plus  the  discounted  value  of  a  perpetual 
annuity  of  $2000  a  year  beginning  twenty  years  in  the 
future.  On  the  five  per  cent  basis,  the  forest  will, 
in  ten  years  from  the  present,  be  worth  about  $32,000 
(this  being  the  discounted  value  of  an  immediate  ten-year 
annuity  of  $1000  followed  by  a  perpetuity  of  $2000). 
Twenty  years  from  the  present,  the  forest  will  be  worth 
$40,000  (this  being  the  discounted  value  of  $2000  a  year 
forever) .  The  forest  land  therefore  rises  gradually  in  value 
from  $20,000  to  $32,000  in  the  first  decade,  during  which  no 
income  is  realized,  and  continues  to  rise,  though  less  rapidly, 
to  $40,000  in  the  second  decade,  during  which  there  is 
realized  the  comparatively  small  income  of  $1000  a  year. 
The  rate  of  return,  therefore,  at  the  beginning,  being  the  quo- 
tient of  the  income  realized  divided  by  the  capital,  is  ^u,, 
or  zero.  The  rate  of  return  evidently  remains  zero  through- 
out the  first  decade.  At  the  beginning  of  the  second  decade 
the  rate  is  evidently  ^~,  or  3.1  per  cent;  at  the  beginning 
of  the  third  decade  it  is  42^,  or  5  per  cent.  We  see, 
therefore,  that  in  this  case  the  rate  of  value-return  gradually 
rises  from  zero  to  a  height  equal  to  the  rate  of  interest. 

There  may  even  be  a  negative  rate  of  return.  A  colt,  for 
instance,  may  occasion  more  trouble  than  it  is  worth  for  the 
first  year,  and  produce  a  net  expense  or  disservice  of  $20. 
Thereafter  it  may  render  a  net  income  of  $10  during  the 
second  year,  $20  during  each  year  from  the  third  to  the 
tenth  inclusive,  and  $10  a  year  the  next  five  years,  after 
which  it  dies.  Supposing,  as  our  preliminary  hypothesis 


SEC.  4] 


EARNINGS   AND   INCOME 


233 


obliges  us  to  do,  that  all  these  arc  definitely  foreseen  at  the 
start,  the  colt  would  be  worth  the  discounted  value  (at  5 
per  cent)  of  all  these,  or  about  $135.  It  will  therefore 
yield  during  the  first  year  a  return  of  :1;^,  or  —  15  per  cent. 
The  value-return  for  the  second  year,  reckoned  on  its  capital- 
value  taken  at  the  beginning  of  that  year,  is  ™v  or  6  per 
cent;  on  the  third  year  ^,  or  13  per  cent,  on  the  fifteenth 
year  about  J-°,  or  100  per  cent.  The  entire  series  may  be 
seen  from  the  following  table :  — 


CAI-ITAL- 

INCOME 

VALI'K    AT 

RATE 

DURING  YEAR 

BEGINNING  OF 

OF  RETI/KN 

YEAH 

1st  year     

-$20 

$134 

-  15% 

2d  year     

10 

161 

6 

3d  j^ear     

20 

159 

13 

4th  year    

20 

146 

14 

5th  year    

20 

134 

15 

6th  year    

20 

121 

17 

7th  year    

20 

107 

19 

8th  year    

20 

92 

22 

9th  year    

20 

76 

26 

10th  year    

20 

60 

34 

llth  year    

10 

43 

23 

12th  year    

10 

35 

28 

13th  year    

10 

27 

37 

14th  year    

10 

19 

54 

15th  year    

10 

10- 

100  + 

From  the  foregoing  examples  it  is  evident  that  a  prop- 
erty which  yields  5  per  cent  to  the  investor  may  yield  in 
individual  years  either  more  or  less  than  5  per  cent.  The 
dwelling  house  yielded  more  than  5  per  cent  for  50  years, 
and  then  ceased  to  yield  income.  The  forest  yielded  less 
than  5  per  cent  for  20  years,  and  thereafter  yielded  5  per 
cent  on  its  value  at  that  time.  The  colt  yielded  rates  ris- 


NATURE    OF    CAPITAL    AND    INCOME       [CiiAP.  XIV 

ing  from  —  15  per  cent  in  the  first  year  to  100  per  cent  in 
the  fifteenth  year,  and  then  zero  forever  after. 

At  this  juncture,  however,  the  business  reader  may  feel 
disposed  to  object.  He  will  point  out  that  in  our  tables  the 
house  is  represented  as  yielding  5.4  per  cent  the  first  year 
instead  of  5  per  cent,  by  neglecting  depreciation,  and 
that,  contrariwise,  the  forest  was  represented  as  yielding  in 
the  eleventh  year  3.1  per  cent  instead  of  5  per  cent,  by 
neglecting  appreciation.  For  it  is  true  that  the  house, 
worth  $18,300  at  the  beginning  of  the  year,  must,  under  the 
given  conditions,  depreciate  $85  during  the  year;  and  the 
objector  will  maintain  that  this  ought  to  be  deducted  from 
the  $1000  received  from  the  house,  in  order  to  obtain  the 
true  "net  earnings."  The  deduction  leaves  $915,  which  is 
just  5  per  cent  on  the  capital  of  $18,300.  According  to  this 
calculation,  therefore,  the  house  really  returns,  not  5.4  per 
cent,  but  only  5  per  cent.  And,  applying  the  same  line 
of  reasoning  to  the  case  of  the  forest,  the  objector  might 
insist  that  the  forest  increased  in  value  just  enough  to 
make  up  the  difference  between  the  3.1  per  cent,  which  was 
given  as  the  rate  of  value-return  at  the  beginning  of  the 
second  decade,  and  the  5  per  cent  to  which  it  would  seem 
to  be  entitled. 

These  calculations  are  correct.  But  they  do  not  mili- 
tate against  the  treatment  of  value-return  which  has  been 
given.  They  merely  bring  into  relief  a  distinction  between 
income  which  is  realized  by  the  investor  and  income  which 
is  earned  by  the  capital.  Realized  income  is  the  value  of 
the  actual  services  secured  from  the  capital;  earned  in- 
come is  found  by  adding  to  realized  income  the  increase 
of  capital-value,  or  deducting  from  it  the  decrease.  We 
may  designate  them  briefly  simply  as  income  and  earning*. 

To  illustrate  this  distinction  and  to  show  its  importance, 
let  us  consider  a  four  per  cent  $1000  bond,  the  interest  on 
which  is  payable  annually.  From  what  was  shown  in  the 
previous  chapter  it  is  clear  that  (if  the  bond  is  valued  on  a 


SEC.  4]  EARNINGS   AND    INCOME  235 

four  per  cent  basis)  the  value  of  the  bond  will  oscillate 
between  $1000  and  $1040,  rising  gradually  from  the  former 
to  the  latter  between  interest  payments  and  falling  back 
suddenly  as  each  payment  is  made.  The  income  is  simply 
the  payment  of  $40  at  the  end  of  each  year.  Even  our 
objector  will  not  deny  this.  During  the  entire  year  up  to 
the  very  end  there  is  no  income  at  all ;  yet  the  bond 
"earns"  about  $10  each  quarter,  in  the  form  of  an  increase 
in  the  value  of  the  bond.  These  earnings  are  simply  equal 
to  the  interest  on  the  capital.  And  so  in  general,  when 
we  assume  that  income  is  definitely  foreknown,  earnings 
will  equal  the  interest  on  the  capital.  It  is,  therefore, 
to  earnings  that  accountants  instinctively  give  their  main 
attention.  But  they  err  grievously  when  they  attempt  to 
spirit  away  realized  income  and  put  earned  income  in  its 
place.  Realized  income  plays  the  more  important  role,  for 
on  it  depend  all  the  other  elements,  — •  capital- value,  value- 
return,  depreciation,  and  even  earnings  themselves.  To 
take  the  case  of  the  house,  the  first  and  primary  fact  is  that 
it  promises  to  yield  $1000  a  year  for  fifty  years.  This  income 
series  being  given,  it  is  possible  to  obtain  its  capital-value 
by  the  discounting  process ;  its  value-return,  by  division  of 
income  by  capital ;  its  depreciation,  by  comparing  its  capital 
values  at  successive  dates;  and  its  earnings,  by  deducting 
depreciation  from  realized  income.  Unless  the  realized 
income  be  given  at  the  start,  all  these  calculations  are  im- 
possible. Earnings  could  not  serve  as  our  starting  point, 
for  earnings  cannot  be  calculated  except  by  the  aid  of  de- 
preciation, depreciation  cannot  be  calculated  except  from 
capital- value,  and  capital- value  cannot  be  calculated  except 
from  expected  realized  income. 

Moreover,  the  fundamental  proposition  of  the  last  chap- 
ter, that  capital-value  is  the  discounted  value  of  expected 
income,  will  cease  to  hold  true,  if  by  income  we  mean 
earnings.  Thus,  the  house  has  a  capital-value  of  $18,300, 
which  is  the  discounted  value  of  its  realized  income  of 


236  NATURE   OF   CAPITAL   AND    INCOME      [CHAP.  XIV 

$1000  a  year  for  20  years,  discounted  at  5  per  cent.  But 
it  is  not  true  that  $18,300  is  the  discounted  value  of  the 
earnings  of  the  house,  for  the  earnings  are  all  less  than 
$1000,  beginning  at  $918  a  year  and  dwindling  each  year 
until  the  fifty  years  have  expired;  and  clearly  the  dis- 
counted value  of  fifty  annual  items  each  less  than  $1000 
must  be  less  than  the  discounted  value  of  fifty  annual  items 
of  $1000  each. 

Since,  then,  earned  income  cannot  be  derived  without 
assuming  realized  income,  and  since  capital-value  has  been 
shown  to  be  the  present  value  of  the  latter,  and  not  of  the 
former,  it  is  clear  that  realized  income  is  the  more  funda- 
mental concept  of  the  two. 

§5 

But  so  persistent  is  the  accountant's  instinct  to  put  aside 
realized  income  in  favor  of  earnings  that  we  need  to  point 
out  in  detail  the  confusions  which  arise,  unless  income  and 
earnings  are  carefully  distinguished.  We  first  observe  that, 
under  the  given  conditions  of  foreknowledge,  earnings  and 
interest  are  equal.  Now  if  interest  is  at  5  per  cent,  a  capi- 
tal of  $1000  invested  in  whatever  form  —  land,  houses, 
horses,  securities,  or  anything  else  —  though  it  is  said  to 
earn  5  per  cent,  does  not  necessarily  receive  an  income  each 
year  of  $50.  The  $1000  means  the  present  value,  dis- 
counted at  5  per  cent,  of  some  expected  income  stream ; 
but  that  income  stream  may  take  any  one  of  an  indefinite 
number  of  forms;  such,  for  instance,  as  a  perpetual  annu- 
ity of  $50  a  year,  as  in  the  case  of  land ;  or  a  terminable 
annuity  of  $100  a  year  for  14  years;  or  an  income  of  $25  a 
year  for  10  years  followed  by  an  income  of  $167.50  a  year 
for  10  years.  All  of  these  are  inter-equivalent,  and  when 
discounted  at  5  per  cent,  each  of  them  represents  a  capital 
of  $1000. 

Of  all  these  possible  forms  of  income  it  is  usual  to  take  the 
perpetual  annuity  as  the  standard  income  (earnings)  and  to 


SEC.  5]  EARNINGS   AND    INCOME  237 

compare  other  incomes  with  it.  Consider,  for  instance,  the 
possessor  of  a  property  yielding  $100  a  year  for  14  years. 
He  will,  if  he  discounts  this  income  at  5  per  cent,  value  that 
property  at  $1000.  He  thinks  of  himself  as  possessing 
$1000  "invested  in"  that  property.  From  it  he  gets  the 
income  of  $100  a  year  for  14  years.  But  he  knows  that  he 
might  sell  this  property  for  $1000  and  reinvest  in  another 
property  yielding  the  standard  $50  a  year  forever.  Con- 
trasting with  the  standard  income  of  $50  a  year  forever 
which  he  might  receive,  the  income  of  $100  a  year  for  14 
years  which  he  does  receive,  we  observe  that  at  first  his  in- 
come is  double  the  earned  or  standard  income,  being  $100 
instead  of  $50.  The  excess  of  $50,  however,  is  compen- 
sated for  by  a  reduction  of  $50  in  the  capital-value  of  his 
property,  for  at  the  end  of  the  first  year  the  value  of  his 
property  will  be  the  discounted  value  of  $100  a  year  for 
thirteen  (instead  of  fourteen)  years,  which,  if  interest  is 
still  reckoned  at  5  per  cent,  is  $950.  And  so  it  is  in  general 
that  the  owner  of  $1000  invested  at  5  per  cent  can  obtain  a 
higher  income  than  the  standard  $50  only  at  the  cost  of 
trenching  on  capital  to  the  extent  of  the  excess. 

Suppose,  on  the  contrary,  that  the  $1000  is  invested  at 
5  per  cent,  but  in  such  a  form  as  to  yield  at  first  less  than 
$50,  e.g.  in  a  form  which  yields  the  above-mentioned  in- 
come of  $25  a  year  for  10  years,  followed  by  $167.50  a  year 
for  10  years.  In  that  case,  during  the  first  year  the  owner 
receives  only  $25  instead  of  $50,  which  is  the  earned  or 
"standard"  income.  But  the  deficiency  of  $25  in  his  in- 
come is  made  up  by  an  augmentation  of  his  capital  by  that 
amount. 

The  principle  is  perfectly  general,  and  perhaps  too 
familiar  to  require  a  rigorous  demonstration,  though  there 
is  no  difficulty  in  framing  one.  We  may  therefore  state :  — 

(1)  When  a  property  yields  a  specified  foreknown  income, 
and  is  valued  by  discounting  that  income  according  to  a 
specified  rate  of  interest,  if  the  income  realized  is  equal  to 


238  NATURE    OF   CAPITAL   AND    INCOME       [CHAP.  XIV 

the  income  earned  (and  hence  equal  to  the  rate  of  interest), 
the  value  of  the  capital  will  remain  at  a  uniform  level. 

(2)  If  realized  income  exceeds  earned  income,  the  value 
of  the  capital  will  be   decreased  by  the  amount   of  the 
excess. 

(3)  If  realized  income  is  less  than  earned  income,  the 
value  of  the  capital  will  be  increased  by  the  deficiency. 

These  principles  hold  true  whether  the  period  for  reckon- 
ing or  compounding  interest  is  a  year,  half  year,  quarter,  or 
any  other  period,  or  shrinks  to  the  vanishing  point  in  the 
case  of  continuous  interest.  A  slight  modification  or 
qualification  in  the  statement  of  these  principles  is,  how- 
ever, necessary  when,  instead  of  there  being  a  rate  of  in- 
terest which  remains  the  same  year  after  year,  there  is  a 
succession  of  different  rates.1 

Expressed  in  a  single  sentence,  the  general  principle 
connecting  realized  and  earned  income  is  that  they  differ 
by  the  appreciation  or  depreciation  of  capital.  It  is  thus 
possible  to  describe  earned  income  as  realized  income  less 
depreciation  of  capital,  or  else  as  realized  income  plus 
appreciation  of  capital.  We  may  therefore  state  anew  the 
fallacy  of  confusing  realized  income  with  earned  income : 
the  fallacy  consists  in  reckoning  depreciation  of  capital 
as  a  part  of  outgo,  or  appreciation  of  capital  as  a  part  of 
income.  This  usage  is  difficult  to  combat,  for  with  many 
it  has  become  habitual.  To  expose  the  fallacy  completely 
will  be  our  object  during  the  remainder  of  this  chapter. 

§6 

We  may  at  the  outset  emphasize  a  fact  already  mentioned 
in  Chapter  VII ;  namely,  that  this  popular  and  erroneous 
usage  is  not  consistently  adhered  to.  A  pension  is  an 
income  the  capital-value  of  which  is  continually  diminish- 

1  The  case  is  discussed  in  the  Appendix  to  Chap.  XIV,  §  1.  For 
practical  purposes,  however,  this  is  a  refinement  into  which  we  sel- 
dom need  to  enter. 


SEC.  0]  KAHNINCJS    AND    INCOME  2.39 

ing.  Yet  even  popular  usage  seldom  or  never  deducts  this 
depreciation  from  the  pension  to  obtain  the  "true"  in- 
come; and  the  reason  we  instinctively  include  (as  we 
ought)  the  whole  of  such  a  pension  in  income,  is  that 
the  depreciation  is  not  actually  offset.  In  ordinary  busi- 
ness, on  the  other  hand,  we  are  accustomed  to  deduct 
depreciation,  because  this  is  usually  offset  by  actual  pay- 
ments into  a  depreciation  fund.  Even  in  this  case  the 
depreciation  is  not  itxelj  an  expense;  but  there  is  a  con- 
comitant expense  approximately  equal  to  it,  in  the  form  of 
payments  into  the  depreciation  fund.  It  thus  makes  all 
the  difference  in  the  world  whether  the  depreciation  fund  is 
actually  maintained,  or  merely  reckoned.  If  a  deprecia- 
tion fund  is  actually  maintained,  the  expense  of  maintain- 
ing it  serves  to  reduce  realized  income  so  as  to  make  it 
coincide  with  earned  income.  In  such  a  case,  therefore,  the 
ideal  earned  income  becomes  realized  in  actual  fact. 

Assuming  a  fixed  rate  of  interest,  the  depreciation  fund 
may  be  defined  as  a  fund  formed  by  accumulating  that 
part  of  income  which  must  be  turned  back  into  capital  in 
order  to  maintain  the  value  of  capital  at  a  fixed  level.  A 
depreciation  fund  is  thus  made  from  annual  contributions 
equal  to  the  excess  of  realized  income  above  earned  in- 
come. If,  instead  of  an  excess,  there  is  a  deficiency,  the 
contributions  to  the  depreciation  fund  become  negative, 
that  is,  instead  of  a  certain  quantity  of  income  being  con- 
verted into  capital,  a  certain  quantity  of  capital  must  be 
converted  into  income. 

Geometrically,  a  depreciation  fund  is  very  simply  repre- 
sented. In  Figure  7  let  the  income  consist  of  the  items 
a,  a',  a",  a"' ,  oiv,  etc.  The  capitalized  value  of  this  in- 
come stream  is  AB.  The  interest  on  AB  is  represented  by 
the  height  AC,  so  that  the  standard  income  would  be 
represented  by  a  series  of  annual  lines  of  the  height  of  the 
dotted  line  CD.  The  excess  of  the  lines  a,  a',  a",  etc., 
above  the  dotted  line  CD  therefore  represents  the  contri- 


240 


NATURE   OF   CAPITAL   AND    INCOME       [CnA.p.  XIV 


butions  to  the  depreciation  fund.  Where  there  is  a  defi- 
ciency, as  in  the  case  of  a'" ,  the  contribution  to  the 
depreciation  fund  is  negative;  that  is,  for  that  particular 
time,  instead  of  some  of  the  income  being  reinvested,  some 
of  the  capital  is  used  as  income,  to  prevent  income  from 
falling  below  the  uniform  level  prescribed  for  it.  The  same 


a 

a1 

a" 

a  "t 

a'v 

av          a  vi         a  vii 

Fia.  7, 

principles  apply  in  case  the  income  is  a  continuous  flow,  as 
shown  in  Figure  8.  Here  the  earned  income  is  represented 
by  the  elevation  of  the  straight  line  CD,  and  the  realized 
income  by  that  of  the  curved  line  EF;  the  deprecia- 
tion fund  is  formed  from  the  successive  differences  be- 
tween these  elevations.  Thus,  if  $1000  of  capital  is  in- 
vested on  a  4  per  cent  basis,  but  so  that  the  returns  are 
riot  $40,  but  $70  a  year  for  twenty-two  years,  the  annual 


SEC.  6] 


EARNINGS   AND   INCOME 


241 


contribution  to  the  depreciation  fund  is  evidently  $30. 
For  at  the  end  of  the  first  year,  before  the  income  is  re- 
ceived, the  capital-value  will,  under  the  supposed  condi- 
tions, become  not  $1070,  but  only  $1040.  The  first  item 
of  income,  $70,  is  then  received.  This  being  deducted 
from  $1040  leaves  $970,  which  is  $30  short  of  the  original 


Fid.  8. 

capital-value.  Consequently  it  is  necessary  to  restore  S30 
to  the  capital,  in  order  to  bring  it  up  to  the  original  level  of 
$1000. 

It  will  evidently  make  no  difference  whether  the  income 
items  are  reinvested  simply  as  additions  to  the  original 
capital,  or  invested  at  the  same  rate  of  interest  in  some  other 
form  of  capital.  The  owner  of  depreciating  machinery  may 


242  NATURE    OF    CAPITAL   AND    INCOME       [CHAP.  XIV 

offset  that  depreciation  by  investing  annually  in  a  few 
new  machines,  or  by  annually  buying  investment  securities. 
The  latter  type  of  investment  is  usually  thought  of  when 
the  phrase  "depreciation  fund"  is  used.  If  the  owner 
of  the  machines  follows  this  procedure,  then  instead  of 
the  original  capital  being  maintained  at  a  fixed  level,  it  is 
continually  decreasing,  while  the  depreciation  fund  is  con- 
tinually increasing  in  such  a  manner  that  the  value  of  the 
two  together  —  the  machinery  and  the  depreciation  fund 
—  remains  constant.  Consequently,  at  the  end  of  the 
income  term,  when  the  value  of  the  original  capital,  the 
machinery,  is  entirely  exhausted,  the  value  of  the  depre- 
ciation fund  in  securities  will  have  exactly  taken  its  place. 
This  fact  is  sometimes  employed  in  the  definition  of  a 
depreciation  fund.  The  fund  is  then  described  as  formed 
of  a  succession  of  payments  out  of  income,  such  that  if 
each  be  accumulated  at  compound  interest  the  total  will 
equal  the  original  capital  at  the  end  of  the  entire  income 
term. 

The  most  common  application  of  a  depreciation  fund  is 
to  a  bond  which  does  not  sell  at  par.  For  instance,  a 
$100  five  per  cent  bond,  when  interest  is  4  per  cent,  will,  if 
it  has  20  years  to  run,  sell  at  $115.  The  interest  at  4  per 
cent  on  this  capital  is  $4.60,  which  shows  that  the  deprecia- 
tion fund,  being  the  difference  between  the  income  and  the 
interest,  is  $5  minus  $4.60,  or  40  cents.  This  item  of  40 
cents  should  annually  be  saved  out  of  the  income  and  rein- 
vested at  4  per  cent,  in  order  that  at  the  end  there  may 
still  remain  a  capital  of  $115.  If  the  last  installment  of 
income  from  the  bond,  $105,  is  treated  as  an  income  like 
the  previous  items,  the  depreciation  fund  is,  in  the  last 
year,  $105  minus  §4.60,  or  $100.40;  that  is,  besides  the  40 
rents  annually  there  should  be  reinvested,  at  the  end  of 
Hie  term  of  the  bond,  the  $100  of  so-called  "principal." 
Thus  we  again  reach  the  reason  that  the  $100  of  the  last 
payment  is  regarded  as  "principal"  or  "capital"  and  not 


SEC.  7]  EARNINGS   AND    INCOME  243 

"income."  It  is  simply  that  this  $100  is  always  supposed 
to  enter  into  the  depreciation  fund,  that  is,  to  be  rein- 
vested and  not  retained  as  income.  In  case  the  bond  is 
sold  at  par  (i.e.  if  it  yields  an  income  equal  to  the 
market  rate  of  interest),  there  is  no  depreciation  fund  ex- 
cept the  "principal"  itself  at  the  end,  when  the  last  item 
of  realized  income  ($105)  exceeds  the  earned  income  of 
$5  by  $100.  This  excess,  being  reinvested  at  the  same 
rate,  5  per  cent,  will  secure  the  continuance  of  the  same 
income. 

The  operation  of  the  depreciation  fund  presupposes  that 
it  is  possible  to  invest  the  small  differences  each  year  in  such 
a  manner  as  to  accumulate  at  compound  interest  at  the 
rate  which  the  original  capital  is  earning.  Such  is  not  al- 
ways the  case,  especially  with  articles  of  wealth,  like  land, 
machinery,  and  so  forth.  In  case  two  different  rates  of  in- 
terest are  involved,  one  for  computing  the  capital-value  of 
the  given  income,  and  another  for  compounding  the  annual 
savings  put  into  the  depreciation  fund,  the  calculation  of 
the  depreciation  fund  will,  of  course,  be  more  complex.1 

§  7 

In  close  relation  to  a  depreciation  fund  is  the  "sinking 
fund"  employed  by  governments  as  a  means  of  meeting 
large  obligations —  in  particular  of  meeting  the  "principal" 
of  public  debts.  Needless  obscurity  has  enveloped  the 
"sinking  fund,"  especially  since  the  intricate  but  fallacious 
theories  of  Price  and  Pitt. 

The  annual  contribution  to  the  depreciation  fund  was  the 
difference  between  the  income  actually  experienced  and 
an  ideal  perpetual  annuity  of  the  same  present  value. 
A  sinking  fund,  however,  is  formed  from  the  difference 
between  income  (or  more  commonly  outgo)  actually  expe- 

1  The  reader  is  referred  to  the  Institute  of  Actuaries'  Text-book, 
Part  I,  London  (Layton),  1901,  where  this  and  other  problems  in  an- 
nuities are  fully  dealt  with. 


244  NATURE   OF   CAPITAL   AND   INCOME       [CiiAF.  XIV 

rienced  and  an  ideal  terminable  annuity  of  the  same  present 
value.  A  government  has  to  meet  a  series  of  expenses 
connected  with  its  bonded  debt.  These  expenses  constitute, 
let  us  say,  a  stream  of  outgo  lasting  ten  years,  and  consisting 
of  nine  equal  payments — nominally  "interest''  —  and  one 
much  larger  payment,  exceeding  the  others  by  the  amount 
of  the  so-called  "principal."  The  sinking  fund  is  merely  a 
device  for  equalizing  all  ten  payments.  If  the  actual  pay- 
ments are  $5000  a  year  for  nine  years  and  $105,000  in  the 
tenth  year  (as  is  the  case  of  10-year  "five  per  cent"  bonds), 
the  ideal  10-year  annuity  equivalent  to  this  series  would, 
on  a  4  per  cent  basis,  be  §13,329.  The  government,  there- 
fore, if  it  would  pay  off  its  debt,  or  rather  provide  for  it  in 
ten  equal  installments,  must  during  each  of  the  first  nine 
years,  besides  paying  the  $5000  to  its  creditors,  pay  into 
the  sinking  fund  $8329.  In  the  tenth  year  the  process  is 
reversed,  and  the  entire  $100,000  then  accumulated  in  the 
sinking  fund  is  taken  to  pay  the  $100,000  of  "principal." 
Hence,  as  applied  to  bonded  debts,  the  sinking  fund  may  be 
defined  as  formed  by  accumulating  an  annual  sum  during 
a  specified  period,  such  that  its  amount  will  just  suffice 
to  extinguish  a  given  sum  at  the  end  of  that  period. 


Depreciation  and  sinking  funds  are  not  the  only  devices 
by  which  uneven  income  streams  may  be,  as  it  were, 
smoothed  out.  Many  other  devices  may  be  employed.  For 
instance,  a  person  engaging  in  an  unusual  expense,  such  as 
that  of  building  a  house,  will  not  allow  this  expense  to 
seriously  interrupt  the  even  flow  of  his  income,  but  will 
provide  for  it  by  some  correspondingly  unusual  item  of  in- 
come. He  may  sell  other  property,  for  instance  railway 
shares ;  the  unusual  sum  he  realizes  on  the  sale  will  then 
offset  the  unusual  outgo  for  the  dwelling.  Or,  he  may 
mortgage  his  dwelling  and  the  land  on  which  it  stands, 
and  pay  the  debt  off  gradually  —  sell  a  claim  upon  the 


SKC.  8]  EARNINGS   AND   INCOME  245 

dwelling  itself  instead  of  selling  some  property  distinct 
from  the  dwelling.  Or  again,  he  may  make  an  ar- 
rangement at  the  outset  to  pay  for  the  house  in  install- 
ments. 

All  of  these  methods  of  maintaining  more  or  less  regu- 
larity of  income  merely  shift  the  burden  of  an  unusual 
expense  from  one  person  to  another.  The  first  method, 
by  which  the  purchaser  of  the  house  raises  the  necessary 
money  by  selling  other  property,  shifts  to  the  buyer  of 
that  property  an  expense  equal  to  that  which  he  himself 
seeks,  for  the  time,  to  avoid.  The  second  method,  that  of 
mortgage,  presupposes  a  money  lender  who  is  ready  to  sup- 
ply the  necessary  funds.  The  money  lender  is  in  this  case 
the  one  who,  for  the  time,  shoulders  the  burden.  The 
third  method,  payment  by  installment,  implies  that  the 
builder  (or  some  other  party)  advances  the  cost  of  the  dwell- 
ing. In  other  words,  the  person  who  attempts  to  smooth 
out  his  own  income  does  so  by  throwing  his  irregularities 
on  some  one  else,  usually  a  banker  or  broker. 

To  society  as  a  whole  such  purely  shifting  devices  are 
inapplicable,  for  society  can  find  no  outside  party  on  whom 
to  shift  the  fluctuations.  There  is,  however,  a  method  by 
which  society's  income  may  be  more  or  less  standardized. 
This  is  by  assorting  and  combining  the  various  instru- 
ments of  capital  wealth  so  that  the  various  income 
streams  may  mutually  compensate.  For  instance,  if  a 
community  owns  iron  mines,  it  has  a  form  of  property 
which,  for  a  time,  probably  yields  more  than  the  standard 
income.  By  the  nature  of  the  case,  every  bucketful  of  ore 
reduces  the  amount  which  the  mine  can  yield  in  future. 
The  mine  is,  in  fact,  a  sort  of  terminable  annuity.  After  it 
is  exhausted  there  will  be  no  further  returns.  The  capital- 
value  of  the  mine  will  therefore  continually  decrease.  On 
the  other  hand,  forest  land  which  is  covered  with  young 
saplings  will  not  begin  to  yield  much  income  for  many 
years.  The  income  from  this  capital  is  therefore  tempo- 


246  NATURE    OF    CAPITAL    AXD    INCOME       [CHAP.  XIV 

rarily  below  the  standard.  A  community  which  owns  both 
mine  and  timber  land  will  consequently  find  that  the  in- 
crease and  decrease  will  offset  each  other,  so  that  its  income 
will  be  more  nearly  standard  than  if  it  merely  possessed 
either  one  without  the  other. 

§  9 

The  last-named  method  is  applied  to  the  case  of  capital 
which  consists  of  a  large  number  of  instruments  in  differ- 
ent stages  of  production  or  consumption.  If  a  weaving 
mill  is  equipped  with  20  looms  of  the  same  degree  of  wear, 
the  value  of  this  plant  will  evidently  depreciate  and  a  de- 
preciation fund  may  be  necessary.  B;it  if  the  20  looms  are 
evenly  distributed  throughout  the  different  stages  of  wear, 
and  if,  for  convenience,  we  assume  that  one  loom  wears 


out  each  year,  no  depreciation  fund  will  be  necessary.  The 
replacement  of  one  loom  annually  is  equivalent  to  such  a 
depreciation  fund,  and  the  capital  is  thereby  maintained  at 
a  constant  level. 

Any  income  stream  whatever,  even  if  its  component 
parts  are  very  irregular,  will,  if  these  parts  are  renewed  at 
frequent  and  regular  intervals,  necessarily  produce  in  total 
a  uniform  or  standard  income.  Let  ABC  (Figure  9)  repre- 
sent an  income  stream  which  at  first  is  negative  and  after- 
ward positive,  such,  for  instance,  as  is  occasioned  by  first 
constructing  and  then  using  a  machine.  Let  an  exactly 
similar  income  stream  A'B'C'  begin  a  short  time  later,  as 
at  A' ,  and  so  on  indefinitely,  at  equal  intervals.  It  is  evi- 
dent that  after  we  have  reached  the  point  C  at  which  our 
first  income  stream  ends,  we  have  a  fairly  uniform  income 


SEC.  0]  EARNINGS   AND    INCOME  247 

ami  outgo,  the  income  at  any  point  consisting  of  the  sum 
of  the  ordinates  above  the  base  line  AC',  and  the  outgo 
of  the  sum  of  the  ordinates  below. 

This  case  brings  into  juxtaposition  two  different  points 
of  view  from  which  the  interest  on  capital  may  be  con- 
sidered. Professor  ,J.  13.  Clark  conceives  of  interest 
as  the  net  difference  between  the  rate  of  total  income 
and  rate  of  total  outgo  at  any  point,  and  compares 
this  net  return  with  the  capital-value  as  it  exists  at  that 
point.  This  concept  treats  the  outgo  or  cost  of  production 
as  simultaneous  with  the  income,  that  is,  it  takes  into  con- 
sideration any  small  section  of  the  curves  in  Figure  9 
contained  between  any  two  vertical  lines  a  short  interval 
apart.  Professor  Bohm-Bawerk,  on  the  other  hand,  always 
thinks  of  cost  of  production  as  preceding  income.  He 
fixes  his  attention  on  the  elementary  income  stream  ABC, 
and  contrasts  the  outgo  or  cost  between  A  and  B  with  the 
later  income  between  B  and  C.  These  two  points  of  view 
are  evidently  quite  reconcilable,  though  their  authors  do 
not  seem  to  have  realized  the  fact.  Each  carries  his  own 
special  point  of  view  throughout  his  treatment  of  capital 
and  interest.  Professor  Bohm-Bawerk  regards  interest  as 
an  agio,  or  premium,  found  by  contrasting  the  positive  in- 
come return  between  B  and  C  with  the  investment  or  outgo 
between  A  and  B,  whereas  Professor  Clark  regards  interest 
as  the  ratio  between  a  perpetual,  uniform  flow  of  income  and 
the  capital- value  of  the  entire  stock.  In  short,  Bohm- 
Bawerk  has  in  mind  what  we  have  called  in  the  previ- 
ous chapter  the  premium  concept  of  interest,  and  Clark, 
the  price  concept  of  interest. 

§  10 

We  have  seen  that  earned  income  is  often  only  an  ideal 
standard,  and  not  to  be  confused  with  actually  realized  in- 
come. Yet  the  confusion  is  common.  Even  Edwin  Can- 


248  NATURE   OF   CAPITAL   AND   INCOME       [CHAP.  XIV 

nan,  who  is  usually  a  safe  guide,  makes  an  error  at  this 
point.  He  states  in  his  Elementary  Political  Economy : l  - 

"If  a  man  has  a  cellar  of  port  wine,  or  a  plantation  of  trees,  the 
annual  increment  of  the  value  of  these  things  is  evidently  part  of  his 
annual  income.  If  he  likes  to  spend  it,  he  can  do  so  without  decreasing 
his  property.  If  he  does  not  choose  to  spend  it,  he  is  engaged  in  a 
form  of  saving  and  is  thereby  adding  to  his  property." 

And  again,  in  "What  is  Capital?"2  he  states,  "The  in- 
come is  divided  into  two  parts,  (1)  the  increase  of  the 
capital,  and  (2)  the  things  enjoyed." 

That  "saving"  or  increase  of  capital  is  not  income  co- 
ordinately  with  ordinary  income  is  evident  from  the  fact 
that  this  item  is  never  discounted  in  making  up  capital- 
value.  As  we  have  seen,  one  of  the  fundamental  charac- 
teristics of  income  is  that  it  is  the  desirable  event  which 
occurs  by  means  of  wealth,  and  for  the  sake  of  which,  con- 
sequently, that  wealth  is  valued.  This  definition  implies 
that  every  item  of  income  is  discounted  in  order  to  obtain 
its  contribution  to  capital- value.  The  mere  increase  or  de- 
crease of  capital- value,  on  the  other  hand,  is  never  thus 
discounted.  Suppose,  for  instance,  with  interest  at  4  per 
cent,  that  a  man  buys  an  annuity  of  $4  a  year,  which 
does  not  begin  at  once  but  is  deferred  one  year.  Since 
this  annuity  will  be  worth  $100  one  year  hence,  its  present 
value  will  be  about  $96,  which,  during  the  ensuing  year, 
will  gradually  increase  to  $100.  If  this  increase  of  value 
of  (about)  $4  is  itself  to  be  called  income,  it  should  be 
treated  like  every  other  item  of  income,  and  should  be  dis- 
counted. But  this  is  absurd.  The  discounted  value  of  $4 
would  be  $3.85,  which,  if  added  to  the  $06,  would  require 
that  the  entire  value  of  the  property  to-day  should  be 
$99.85,  or  practically  the  same  as  a  year  later  instead  of 
$4  less  as  is  actually  the  case.  In  other  words,  the  hy- 
pothesis which  counts  an  increase  of  value  as  income  is 
self-destructive;  for  if  the  increment  is  income,  it  must 

1  p.  59.  2  Economic  Journal,  Vol.  VII,  1897,  p.  284. 


SEC.  11]  EARNINGS   AND   INCOME  249 

be  discounted,  hut,  if  discounted,  it  is  practically  abolished. 
Clearly,  then,  increase  of  capital  is  not  income  in  the  sense 
that  it  can  be  discounted  in  addition  to  other  items  of  in- 
come. If  it  is  income  at  all,  it  is  income  in  a  very  peculiar 
sense,  and  nothing  but  confusion  can  result  from  having 
to  consider  two  kinds  of  income  so  widely  divergent  that 
whereas  one  is  discounted  to  obtain  capital- value,  the  other 
is  not. 

We  have  seen  that  the  increase  of  capital  is  at  the  ex- 
pense of  income.  It  is  occasioned  by  and  is  equal  to 
the  deficiency  of  realized  compared  with  standard  income. 
With  this  in  mind,  Edwin  Cannan's  definition  of  income 
could  be  stated  as  realized  income  plus  the  deficiency  be- 
tween realized  and  earned  income.  But  this  is  earned 
income,  not  realized  income. 

§11 

To  put  the  matter  in  a  practical  light,  let  us  imagine  the 
case  of  three  brothers,  each  of  whom  inherits  the  same 
fortune,  say,  $10,000.  Let  us  assume  that  interest  is  5  per 
cent.  The  first  brother  invests  his  $  10, 000  in  an  annual 
annuity  of  $500  a  year  forever.  The  second  puts  his  in 
trust  to  accumulate  at  5  per  cent  for  fourteen  years,  at 
which  time,  having  doubled  in  value,  it  is  to  be  invested 
in  a  perpetual  annuity  of  81000  a  year.  The  third,  being 
of  the  spendthrift  type,  buys  an  annuity  of  $2000  a  year  for 
(nearly)  six  years. 

According  to  the  theory  here  advocated,  the  first  has 
a  perpetual  income  of  $500  a  year;  the  second  has  no 
income  for  14  years,  and  thereafter  an  income  of  $1000 ; 
the  third  has  an  income  of  $2000  a  year  for  6  years  and 
thereafter  none  at  all.  This  mode  of  viewing  the  matter 
also  squares  with  ordinary  business  reckoning. 

On  the  other  hand,  according  to  the  theory  which  re- 
gards increase  of  capital  as  income,  although  the  income 
from  the  first  would  be  the  same  as  we  have  reckoned  it, 


250  NATURE    OF    CAPITAL   AND    INCOME       [CHAP.  XIV 

that  of  the  second  and  third  would  be  quite  different :  the 
income  of  the  second  would  be  $500  the  first  year,  for  during 
that  year  his  capital  increases  from  $10,000  to  $10,500; 
it  would  be  $525  the  second  year,  during  which  his  capi- 
tal increases  again  from  $10,500  to  $11,025,  and  so  on, 
until  in  15  years  he  is  receiving  an  income  of  $1000  a  year. 
The  third  brother,  during  the  first  year,  uses  $2000;  but 
as  his  interest  is  only  $500  he  is  forced  to  take  $1500  out  of 
capital.  This  is,  in  our  view,  true  realized  income.  But  ac- 
cording to  the  theory  which  we  are  criticising,  this  deprecia- 
tion of  $1500  would  have  to  be  deducted  from  the  $2000 
which  the  spendthrift  actually  enjoys,  in  order  to  compute 
his  net  income.  The  net  income  would  thus  be  only  $500, 
or  the  interest  on  his  original  capital.  At  the  beginning 
of  the  second  year,  this  spendthrift  brother  would  possess 
a  capital  of  $8500,  the  " income"  of  which  would,  by  the 
same  theory,  be  5  per  cent  on  $8500,  or  only  $425.  Follow- 
ing similar  reasoning  to  the  end  we  find  that  the  so-called 
"income"  would  progressively  diminish  until,  in  the  sixth 
year,  it  would  be  only  $90.  The  capital  then  having  been 
entirely  destroyed,  no  income  would  remain.  It  would  ap- 
pear from  all  this  that  the  spendthrift  had  received  from 
the  original  $10,000,  during  the  six  years  of  its  life,  a  very 
small  income,  steadily  diminishing  from  $500  to  zero,  the 
sum  total  being  only  $1695.  Was  it  for  such  an  "income" 
that  he  invested  $10,000  ? 

§12 

If  we  suppose  an  income  tax  laid  on  the  three  brothers,  we 
shall  find  that,  according  to  the  different  interpretations 
which  we  give  to  the  term  "income,"  the  results  will 
be  startlingly  different.  If  the  income  be  taken  in  its  true 
sense,  namely,  as  those  items  whose  capital-value  is  the 
$10,000  with  which  the  three  brothers  started,  then  an  in- 
come tax  of  10  per  cent  will  yield  from  the  first  brother 
$.50  a  year;  from  the  second,  nothing  for  14  years,  after 


SEC. 12] 


KAHMNGS    AND    INCOME 


251 


which  it  will  yield  $100  a  year;  and  from  the  third,  §200 
a  year  for  6  years1  and  nothing  thereafter.  The  burden 
of  the  three  taxes  on  these  three  brothers  will  under  these 
conditions  be  exactly  equal,  when  the  three  are  compared 
by  means  of  their  present  values.  Each  brother  could 
"compound"  for  his  taxes  (that  is,  could  pay  a  fixed  sum 
in  advance  in  lieu  of  the  annual  sums)  at  the  same  cost, 
namely,  $1000;  for  $1000  is  the  sum  in  present  cash  which 
is  equivalent  respectively  to  $50  a  year  forever;  to  $100  a 
year  beginning  14  years  hence;  and  to  $200  a  year  for  0 
years.  But  turning  now  to  the  spurious  interpretation  of 
income  as  the  value  of  uses  plus  the  accumulation  of  capi- 
tal, or  the  value  of  uses  less  the  depreciation  of  capital,  we 
find  that  the  three  brothers  would  be  very  unequally  taxed. 
The  first  would,  as  before,  pay  $50  a  year  indefinitely. 
But  the  second  who  "saves"  for  14  years,  will  be  compelled 

SECOND  BROTHER 


CAPITAL 

SO-CALLED 

"  IscoMK" 

TA  x 

TlIKKEOX 

TRUE 
INCOME 

TAX 

TlIKKEOX 

At  beginning      .     . 

810,000 

In     1  year      .     .     . 

10,500 

S500 

S50.00 

nil 

nil 

In    2  years    .     .     . 

1  1  ,02.5 

525 

52.50 

nil 

nil 

In    3  years    .     .     . 

11,576 

551 

55.10 

nil 

nil 

In    4  years    .     .     . 

12,155 

579 

57.90 

nil 

nil 

In    5  years    .     .     . 

12,763 

608 

60.80 

nil 

nil 

In    0  years    .     .     . 

13,401 

638 

63.80 

nil 

nil 

In    7  years    .     .     . 

14,071 

670 

67.00 

nil 

nil 

In    8  years    .     .     . 

14,775 

704 

70.40 

nil 

nil 

In     9  years    .     .     . 

15,513 

733 

73.80 

nil 

nil 

In  10  years    .     .     . 

16,289 

776 

77.60 

nil 

nil 

In  11  years    .     .     . 

17.  1015 

S16           81.60 

nil 

nil 

In  12  years    .     .     . 

17.059 

856 

85.60 

nil 

nil 

In  13  years    .     .     . 

18,856 

897            89.70 

nil 

nil 

In  14  years    .     .     . 

19,799 

943           94.30 

nil 

nil 

In  14i  years  .     .     . 

20,000 

nil             nil 

Thereafter      .     .     . 

20,000 

1000 

100.00 

S1000    :     $100 

1  Or,  to  be  exaet,  ?200  a  year  for  5  years  and  ?1SO  in  the  last  year, 
inasmuch  as  the  capital  will  be:  exhausted  in  a  little  less  than  6  years. 


252 


NATURE    OF    CAPITAL   AND   INCOME      [CHAP.  XIV 


to  pay  an  annually  increasing  tax  on  this  saving  for  the  14 
years  of  postponement,  and  then  a  tax  on  the  income  from 
these  same  savings  in  which  his  annuity  is  to  consist. 
His  first  year's  savings  will  be  $500  and  will  be  taxed  $50. 
During  the  second  year  his  capital  grows  from  $10,500  to 
$11,025,  making  an  increase  of  $525,  the  tax  on  which  is 
$52.50,  and  so  on,  as  shown  in  the  preceding  table. 

The  third  brother,  under  such  a  tax,  will  fare  as  shown 
below :  — 

THIRD  BROTHER 


CAPITAL 

SO-CALLED 
"  INCOME" 

TAX 

THEREOF 

TRUE 
INCOME 

TAX 

THEHEOX 

At  beginning 

$10,000 

In  1  year 

8,500 

$500 

$50.00 

$2,000 

$200 

In  2  years 

6,930 

425 

42.50 

2,000 

200 

In  3  years 

5,270 

340 

34.00 

2,000 

200 

In  4  years 

3,530 

260 

26.00 

2,000 

200 

In  5  years 

1,710 

180 

18.00 

2,000 

200 

In  6  years 

nil 

90 

9.00 

1,800 

180 

Thereafter    .     .     . 

nil 

nil 

nil 

nil 

nil 

When  we  compare  the  burden  of  the  various  taxes  im- 
posed on  so-called  "  income,"  we  shall  find  that  the  first 
brother  could  " compound"  for  his  taxes,  as  before,  by  a 
cash  payment  of  $1000.  The  second  brother,  however, 
would  need  to  pay  $1714.  For  he  would  have  to  pay  $1000 
as  the  present  value  of  the  tax  of  $100  a  year  beginning  in 
14  years,  and  in  addition,  $714  as  the  present  value  of 
the  series  of  taxes  on  his  savings,  namely,  $50,  $52.50.  etc. 
And  the  third  brother,  though  the  least  provident  of  all, 
could  compound  for  only  $157.73,  this  being  the  present 
value  of  the  six  small  tax  payments  which  he  would  have 
to  make,  namely,  $50,  $42.50,  $34,  $26,  $18,  and  $9.' 

1  In  the  foregoing  calculation  it  was  assumed  that  the  tax  did  not 
itself  affect  the  value  of  the  "income"  on  which  the  tax  is  laid.  But 
this  would  be  untrue  of  "income"  which  includes  the  increment  of 
capital.  For  the  discussion  of  this  point,  see  Appendix  to  Chap. 
XIV,  §  2. 


SEC.  1.",]  EARNINGS   AND    INCOME  253 

Instead,  therefore,  of  having  a  burden  of  taxes  on  the  three 
brothers,  all  of  which  have  an  equal  present  value  of  $1000, 
we  find  the  unequal  burdens  of  SI 000,  $1714,  and  S157.73. 
Such  a  system  of  taxation  is  clearly  unjust  and  discour- 
ages the  saver,  while  it  encourages  the  spendthrift.  The 
spendthrift  virtually  has  some  of  his  taxes  remitted  to  him, 
whereas  the  saver  is  made  the  victim  of  that  too  frequent 
concomitant  of  fallacious  economic  theory,  —  double  taxa- 
tion ;  for  he  is  first  taxed  15  years  on  his  accumulation  of 
capital  ($10,000  in  all),  and  thereafter  is  taxed  again  on 
the  income  which  he  derives  from  that  same  accumulation. 
And  yet  this  procedure  is  very  common  in  practice.  It 
amounts  to  taxing,  not  the  income  actually  flowing  from 
capital,  but  its  ''earnings"  or  the  interest  upon  the  cap- 
ital. It  is  familiar  in  the  " general  property  tax"  in 
the  United  States.  Under  it  such  wealth  as  temporarily 
unproductive  land  is  taxed,  though  it  bears  no  income  ex- 
cept the  purely  constructive  income  of  its  annual  rise  in 
value.  To  some  extent  also  the  British  income  tax  is  an 
instance  of  the  same  fallacy. 

§  13 

In  the  example  which  has  been  given  we  have  supposed 
each  brother  to  be  possessed  of  a  fixed  and  definite  annuity. 
We  have  considered  the  effect  of  an  income  tax  on  these 
properties,  according  to  the  incorrect  interpretation  of 
"income."  It  often  if  not  usually  happens,  however,  that 
the  owner  of  a  property  may  use  it  in  any  one  of  many  ways, 
and  thus  derive  from  it  any  one  of  many  income  streams. 
We  have  seen  in  the  previous  chapter  that  the  choice  be- 
tween the  different  methods  of  using  the  property  will  de- 
pend on  the  question,  Which  source  of  income  possesses  the 
greatest  present  value  ?  An  income  tax  laid  according  to 
the  correct  idea  of  income  would  not  disturb  the  com- 
parative merits  of  these  different  income  streams;  but  if 
income  be  interpreted  to  include  savings,  the  tax  would 


254  NATURE    OF   CAPITAL   AND    INCOME      [CHAP.  XIV 

disturb  them  greatly.  The  effect  of  such  a  tax  as  was 
illustrated  in  the  example  of  the  three  brothers  would  be  to 
discourage  the  uses  of  capital  which  involve  waiting.  In 
fact,  this  discouraging  effect  is  well  recognized  and  ap- 
plauded by  the  single-tax  advocates,  although  they  over- 
look the  inequities  involved.  According  to  them,  it  is 
right  to  discourage  waiting,  and  no  speculation  in  real  estate 
such  as  was  described  in  a  previous  chapter  should  be  per- 
mitted. They  would  tax  all  increase  of  value  of  land  in  the 
manner  just  described.  Perhaps  the  most  harmful  case  of 
such  a  system  of  taxation  is  that  of  forest  land.  Forestry 
advocates  have  long  been  aware  of  the  baleful  effect  of  the 
taxation  of  growing  forests,  producing,  as  it  does,  wasteful 
and  premature  cutting,  and  have  attempted  to  secure  a 
reduction  or  remission  of  such  taxes.  But  the  persistent 
belief  that  the  annual  increment  of  value  of  such  forests  is 
income  and  should  be  taxed  has  hitherto  prevailed  in 
America,  with  the  natural  consequence  that  the  owners  of 
these  forests  have  cut  them  when  they  should  have  allowed 
them  to  grow.  In  Europe,  a  longer  experience  in  forestry 
has  led,  in  some  cases,  to  a  more  rational  system.  "  Baden 
exempts  newly  established  forests  from  tax  for  twenty 
years  (law  of  1886).  In  Austria  they  are  exempt  for 
twenty-five  years  (law  of  1869).  In  France  three-fourths 
of  the  land  tax  is  remitted  for  thirty  years."1  Even  a 
small  tax,  when  laid  on  forest  land  which  will  yield  no 
timber  for  fifty  years,  becomes  a  very  serious  drain  in  the 
long  run.2 

§  14 

The  fallacy  which  has  been  exposed  is  not  only  a  con- 
fusion between  realized  and  earned  income;  it  is  also  a 
confusion  between  income  and  capital.  To  regard  "sav- 

1  "  How  shall  Forests  bo  Taxed  ?  "  }>y  Alfred  Gaskill,  Forestry  ami 
Irrigation,  April,  190(3,  p.  17o. 

•  Sonic  limitations  on  the  applications  of  a  theoretical!}'  correct  in- 
come tax  are  mentioned  in  the  Appendix  to  Chap.  XIV,  §  3. 


SKC.  14]  EARNINGS   AND    INCOME  255 

ings"  as  income,  is  essentially  to  regard  an  increase  of 
capital  as  income.  Hut  from  what  has  been  said  it  is  clear 
that  he  who  increases  his  income  must  decrease  his  capital 
to  an  equal  extent.  Capital  and  income  are  thus  mutually 
exclusive.  One  cannot  receive  the  whole  standard  income, 
and  at  the  same  time  secure  also  an  increase  of  his  capital. 
Trie  truth  of  this  has  been  instinctively  expressed  in  the 
adage,  "  You  cannot  eat  your  cake  and  have  it  too." 

We  have  learned,  then,  to  distinguish  between  standard 
and  realized  income.  The  one  is  ideal,  the  other  actual. 
The  one  is  that  income  which,  if  it  were  received,  would 
leave  the  level  of  capital- value  unchanged ;  the  other  is  that 
income  which  is  actually  received  and  detached  from  capi- 
tal, no  matter  whether  that  capital,  as  a  result,  is  increased 
or  decreased.  In  short,  the  one  is  earned,  the  other  realized. 

The  t\vo  may,  of  course,  coincide,  in  which  case  capital- 
value  remains  constant.  When  they  do  not  coincide,  the 
discrepancy  measures  the  increase  or  decrease  of  capital- 
value.  This  discrepancy  may  be  partially  or  wholly  done 
awray  with  by  means  of  a  depreciation  fund  or  other  de- 
vices whereby  realized  income,  otherwise  irregular,  is  made 
regular.  But,  merely  to  reckon  depreciation  is  not  to  pro- 
vide for  it.  It  merely  stigmatizes  part  of  realized  income 
as  "coming  out  of  capital,"  but  it  does  not  make  good 
the  loss  of  capital  nor  prevent  its  becoming  a  part  of 
realized  income.  No  more  does  the  mere  calling  of  "sav- 
ings" by  the  name  of  income  make  it  realized  as  income. 
These  two  procedures  are  both  attempts  to  standardize 
income  in  thought  when  it  is  not  standardized  in  fact. 
We  have  seen  that  they  represent  a  confusion  both  be- 
tween capital  and  income  arid  between  income  which  is 
merely  earned  and  income  which  is  actually  realized,  and 
that  they  lead  to  inequitable  taxation  —  double  taxation 
to  the  saver  and  remission  of  taxes  to  the  spendthrift. 


CHAPTER  XV 

CAPITAL   AND   INCOME   ACCOUNTS 


THE  last  two  chapters  have  their  counterpart  in  account- 
ing. Correctly  kept  accounts  will  show  that  an  abnormal 
increase  of  income  is  always  at  the  expense  of  capital.  In 
the  case  of  a  corporation,  the  distribution  among  the  stock- 
holders of  such  excessive  income  is  called  "paying  divi- 
dends out  of  capital."  It  is  not  necessarily  or  always 
wrong.  A  Land  Company  of  California  has  already  been 
cited  as  a  legitimate  case.  A  case  at  the  opposite  ex- 
treme would  be  one  in  which  the  dividends  are  made 
unusually  small  in  order  that  the  capital  may  be  in- 
creased. There  is  in  New  York  City  a  company  which 
has  never  declared  any  dividends,  but  has  been  rolling  up 
a  large  surplus  for  years,  and  whose  stock  is  for  this  reason 
much  above  par. 

We  have  already  seen  in  Chapter  VIII,  that  every  item 
in  an  income  account  represents  the  income  or  outgo  from 
some  item  in  the  capital  account.  That  is,  the  income  ac- 
count consists  merely  in  a  statement  of  the  income  and 
outgo  connected  with  each  item  of  asset  or  liability,  includ- 
ing that  class  of  assets  and  liabilities  which  are  alike  claims 
and  obligations,  such  as  leases  and  employees'  contracts. 
If  the  income  for  each  item  remains  steady  or  standard,  the 
relation  between  the  capital  and  income  accounts  is  very 
simple.  In  such  a  case  (supposing  the  rate  of  interest  to 
be  5  per  cent),  each  item  in  the  capital  account  will  con- 
stantly stand  at  twenty  times  the  amount  of  the  corre- 

256 


SEC.  2]  CAPITAL   AND    INCOME    ACCOUNTS  257 

sponding  item  in  the  income  account.  Let  us  suppose  a 
factory  company  operating  a  plant  worth  $300,000,  which 
is  bonded  for  $100,000.  The  remainder,  $200,000,  will 
represent  the  capital  and  surplus  of  the  company  If  these 
valuations  represent  a  true  and  not  simply  a  fictitious  book 
value,  and  if  the  rate  of  interest  be  taken  at  5  per  cent,  the 
fact  that  the  plant  is  worth  $300,000  signifies  simply  that 
its  earning  power  is  $15,000  a  year,  of  which  $5000  goes 
in  interest  to  the  bondholders  and  $10,000  in  dividends 
to  the  stockholders.  The  capital  and  income  accounts  of 
such  a  firm,  doing  a  steady  and  uninterrupted  business, 
would  repeat  themselves  in  monotonous  regularity  year 
after  year. 

§<-> 
2 

If  now  we  suppose  that  the  repairs  and  replacement  of 
the  plant  do  not  occur  in  equal  amounts  each  year,  but  that 
it  is  necessary,  at  long  intervals,  to  make  large,  special,  or 
extraordinary  repairs ;  there  will  occur  during  the  interme- 
diate years  " depreciations"  of  the  plant,  and  sudden  res- 
torations in  its  value  when  these  special  repairs  are  made. 
Thus,  suppose  that  during  the  year  1900,  the  factory 
depreciates  by  $10,000.  The  capital  account  at  the  begin- 
ning and  end  of  this  year,  and  the  income  account  during 
the  year,  will  be  given  in  the  following  table :  — 

CAPITAL  ACCOUNT  AT  BEGINNING  OF  YEAR  1900 
Assess  Liabilities 

Factory $300,000    Bonds        8100,000 

Capital  and  surplus    .       200,000 

S300,000  8300,000 

CAPITAL  ACCOUNT  AT  EXD  OF  YEAR  1900 
Assets  Liabilities 

Factory 8290,000    Bonds         §100,000 

Capital  and  surplus     .      190.000 

$290,000  $290,000 


258  NATURE    OF   CAPITAL   AND   INCOME         [CHAP.  XV 

INCOME  ACCOUNT  DURING  YEAR  1900 

Capital  Source  Income  Outgo  Net 

Factory  Product  .     840,000     Running    ex- 

penses    .     .  SI 5, 000  +  $25,000 

Bonds  Interest     .     .       5,000       -  5,000 

Capital  and 

Surplus  Dividends      .     20,000    -  20,000 


$40,000  $40,000  000 

From  this  table  we  see  that  the  factory  yields  §25,000; 
as  it  is  worth  only  $300.000  (on  a  5  per  cent  basis),  by  the 
principles  of  Chapter  XIV,  it  cannot  yield  more  than 
$15,000  without  depreciating  to  the  extent  of  the  dif- 
ference ($10,000);  but,  instead  of  setting  aside  something 
for  depreciation,  i.e.  to  pay  for  future  repairs,  the  com- 
pany has  declared  larger  dividends.  Hence,  corre- 
sponding to  the  depreciation  of  $10,000  in  the  value  of  the 
plant  there  is  an  excess  of  $10,000  above  the  "standard" 
income  received  by  the  stockholders.  Instead  of  $10,000, 
which  is  the  normal  interest  on  their  capital  and  surplus  of 
$200,000,  they  receive  $20,000.  The  extra  $10,000  above 
the  standard  thus  corresponds  precisely  to  the  depreciation 
of  their  property,  which  accordingly  sinks  in  the  course 
of  the  year  from  $200,000  to  $190,000. 

During  the  next  year  we  shall  suppose  that  the  factory 
yields  again  $25,000.  Since  its  value  was,  at  the  beginning 
of  the  year,  $290,000,  it  cannot,  on  a  5  per  cent  basis,  yield 
more  than  $14,500  without  depreciating  to  the  extent  of 
the  difference  (in  this  case  $25,000 -$14,500,  or  $10,500). 
Its  value  at  the  end  of  the  year  exclusive  of  improvements 
is  consequently  $290 ,000 -$10,500,  or  $279,500.  We  shall 
suppose  that  the  entire  depreciation  for  the  two  years, 
820,500,  is  made  good  by  extraordinary  repairs  to  that 
amount.  .Since  the  factory  yields  only  $25,000  and  only 
$20,000  after  the  bondholders  are  paid,  it  will  be  necessary, 
in  order  to  meet  the  $20,500  of  repairs  to  assess  the  stock- 
holders $500.  The  accounts  will  then  stand  as  follows  :  — 


SEC.  3]  CAPITAL   AND   INCOME   ACCOUNTS 

CAPITAL  ACCOUNT  AT  BEGINNING  OF  YEAR  1901 
Assets  Liabilities 

Factory $290,000     Bonds        $100,000 

Capital  and  surplus    .        190,000 

$290,000  $290,000 

CAPITAL  ACCOUNT  AT  END  OF  YEAR  1901 
Assets  Liabilities 

Factory $300,000     Bonds        $100,000 

Capital  and  surplus    .       200,000 

$300,000  $300,000 

INCOME  ACCOUNT  DURING  YEAR  1901 

Capital  Source  Income  Outgo  Net 

Factory        Product  .     $40,000     Running     ex- 
penses     .     .      $15,0001, 
Special  repairs  .        20,500  J    " 

Bonds  Interest       .     .          5,000       -  5000 

Capital  and 

surplus   Assessment  500     Dividends   .     .  000         +  500 


$45,500  $45,500  000 

§   3 

Had  the  repair  bill  been  distributed  over  the  two  years, 
the  dividends  to  the  stockholders,  instead  of  being  $20,000 
the  first  year  and  less  than  nothing  the  second,  would  have 
been  S10,000  in  each.  In  order  to  make  their  income  thus 
stable  and  ''standard"  instead  of  irregular,  it  is  only  neces- 
sary to  employ  a  special  repair  fund.  This  accumulates  for 
a  few  years  as  a  separate  investment,  and  is  then  con- 
verted back  into  the  plant  itself,  which  meanwhile  will 
have  continued  its  depreciation.  We  shall  assume  that  this 
plan  is  adopted,  beginning  with  the  year  1902,  for  which  the 
capital  and  income  accounts  will  be  as  follows :  — 

CAPITAL  ACCOUNT  AT  BEGINNING  OF  YEAR  1902 
Assets  Liabilities 

Factory 8300,000     Bonds        $100,000 

Capital  and  surplus    .       200,000 

8300,000  8300,000 


260  NATURE   OF   CAPITAL   AND    INCOME         [CuAP.  XV 

CAPITAL  ACCOUNT  AT  END  OP  YEAR  1902 
Assets  Liabilities 

Factory $290,000     Bonds        §100,000 

Repair  fund    ....         10,000     Capital  and  surplus    .       200,000 

$300,000  $300,000 

INCOME  ACCOUNT  DURING  YEAR  1902 

Capital  Source  Income  Outgo  Net 

Factory  Product  .     $40,000     Running    ex- 

penses   .     .  $15,000    +$25,000 

Repair  fund  Investment      .     10,000      -  10.000 

Bonds  Interest     .     .       5,000       -  5,000 

Capital  and 

surplus  Dividends      .     10,000     -  10,000 


$40,000  $40,000  000 

Here  we  see  that  the  value  of  the  plant  depreciates  by 
$10,000  as  before,  but  that,  to  replace  the  loss,  there  are 
$10,000  worth  of  repair  funds  invested  in,  say,  stocks  and 
bonds.  The  consequence  of  the  repair  fund  is  that  the  value 
of  the  assets  of  the  company  remains  stationary  at  $300,000  ; 
the  share  of  this  property  which  falls  to  the  stockholders 
also  remains  at  a  constant  level,  namely,  $200,000;  and 
the  stockholders  receive  dividends  of  only  $10,000  instead 
of  $20,000,  having  set  aside  $10,000  to  invest  in  their 
repair  fund.  We  may  suppose  that  during  the  next  year 
the  depreciation  continues  and  that  the  factory  yields  again 
$25,000,  as  we  saw  in  §  2.  Since  its  value  was  only  $290,000, 
the  "earnings"  of  which  are  only  $14,500,  it  must  have 
depreciated  $  10,500.  Since  the  repair  fund  set  aside  in  the 
previous  year  has  earned  5  per  cent,  or  $500,  the  accounts 
for  the  year  1903  will  now  be  as  follows :  — 

CAPITAL  ACCOUNT  AT  BEGINNING  OF  YEAR  1903 
Assets  Liabilities 

Far-tory $290,000     Bonds        $100,000 

Re-pair  fund    ....          10,000     Capital  and  surplus    .       200,000 

$300,000  $300,000 


SEC.  ;J] 


CAPITAL    AND    INCOME    ACCOUNTS 


261 


CAPITAL  ACCOUNT  AT  END  OF  YEAR  1903 

Assets  Liabilities 

Factory $279,500      Bonds        $100,000 

Repair  fund    ....          20,500     Capital  and  surplus     .       200,000 


$300,000 

INCOME  ACCOUNT  DURING  YEAR  1903 


Out  (jo 


§300,000 


Net 


Capital  Source  Income 

Factory  Product  .     $40,000     Running 

expenses      $15,000      +$25,000 
Repair  fund     Interest  New  invert- 

received  500         ment        .        10,000  1 

Interest    re-  j.     -  10,000 

invested  .  500  j 

Bonds  Interest      .         5,000         -  5,000 

Capital  and 

surplus  Dividends          10,000        -  10,000 


$40,500 


$40,500 


000 


Here  we  see  that  the  repair  fund  has  absorbed  in  outgo 
another  $10,000  of  new  investment,  and  that  it  has  yielded 
an  income  of  $500,  which,  however,  has  been  immediately 
reinvested  and  appears  as  outgo  also.  The  consequence  is 
that  in  the  capital  account  at  the  end  of  the  year,  the  factory, 
which  has  depreciated  now  to  $279,500,  has,  synchronously 
with  its  depreciation,  acquired  a  repair  fund  enough  to 
bring  up  the  total  value  of  the  assets  to  $800,000.  The 
value  to  the  stockholders,  therefore,  remains  stationary  at 
$200,000,  on  which  amount  they  have  received  their  stand- 
ard income  of  $10,000. 


During  the  next  year,  we  shall  suppose,  the  extraor- 
dinary repairs  again  need  to  be  made.  Inasmuch  as  during 
this  year  the  plant  has  continued  to  depreciate,  the  special 
repairs  will  amount,  approximately,  to  $31,500,  whereupon 
the  repair  fund  is  sold  and  the  cash  employed  in  actual 
repairs.  The  accounts  for  the  year  1904  will  then  be  as 
follows :  — 


262  NATURE   OF   CAPITAL   AND   INCOME         [CHAP.  XV 

CAPITAL  ACCOUNT  AT  BEGINNING  OF  YEAR  1904 
Assets  Liabilities 

Factory $279,500     Bonds        $100,000 

Repair  fund         .     .     .         20,500     Capital  and  surplus    .       200,000 

$300,000  $300,000 

CAPITAL  ACCOUNT  AT  END  OF  YEAR  1904 
A  ssets  Liabilities 

Factory    (exclusive    of 

improvements)     .     .     $268,500     Bonds        $100,000 

Improvements     .     .     .  31,500     Capital  and  surplus    .       200,000 

Repair  fund    ....  000 

$300,000  $300,000 

INCOME  ACCOUNT  DURING  YEAR  1904 
Capital  Source  Income  Outgo  Net 

Factory  Product  .     $40,000     Running 

expenses        $15,000) 
Special    re-  \  -$6,500 

pairs       .          31,500j 
Repair  fund     Sale   of 

entire  New  in- 

fund  in  vest- 

Dec.     .       31,500         ment       .       10,000    ) 
Interest  .         1,000     Interest      .         1,000    j  +21>50 
Bonds  Interest      .         5,000         -  5,000 

Capital  and 

surplus  Dividends  .       10,000       -  10,000 

$72,500  $72,500  000 

Here  we  see  that  during  the  year  1904,  the  value  of  the 
factory  at  the  beginning  was  $279,500,  and  at  the  end, 
exclusive  of  improvements,  $268,500.  But  the  improvements 
or  special  repairs  amounting  to  $31,500  have  made  up  the 
total  value  of  the  factory  to  $300,000.  There  is  at  this  time 
no  repair  fund  whatever,  as  it  has  all  been  absorbed  in 
improving  the  factory.  The  assets,  therefore,  amount  to 
$300,000;  the  property  of  the  stockholders  remains  sta- 
tionary as  before  at  $200,000;  and  their  dividends  also 
remain  stationary  at  $10,000.  The  factory  itself  during  this 


SBC.  5]  CAPITAL    AND    INCOME    ACCOUNTS  263 

year  does  not  yield  the  §25,000  which  has  regularly  ap- 
peared as  the  net  income  in  the  previous  accounts,  for  during 
this  year  we  have  to  charge  to  the  factory  the  special  repairs 
of  §31,500.  The  factory  itself,  therefore,  produces  a  net 
deficit  of  SG500,  offset  by  the  large  proceeds  received  from 
the  sale  of  the  repair  fund  of  S3 1,500,  which,  less  the  new 
investment  of  §10,000  during  the  year,  shows  a  net  return 
for  the  year  of  §21,500.  We  see,  therefore,  that  the  exist- 
ence of  the  repair  fund  to  cover  depreciation  virtually 
maintains  the  capital  accounts  at  a  constant  level,  merely 
changing  from  year  to  year  the  form  of  the  items,  but  not 
affecting  either  the  interest  of  the  bondholders  or  the 
dividends  of  the  stockholders.  In  other  words,  the  repair 
fund  acts  as  a  means  of  standardizing  the  stockholders' 
income.  In  ordinary  business  accounting,  such  standard- 
izing is  regarded  as  sound  policy. 


Certain  exceptions  occur,  as  in  the  case  of  mining  com- 
panies or  land  companies  which  necessarily  must  terminate 
their  operations  in  the  more  or  less  remote  future.  But 
even  in  such  instances,  the  instinct  of  the  accountant 
toward  standard  accounting  is  so  strong,  that  he  usually 
treats  the  excess  or  deficiency  of  real  income  with  relation 
to  standard  income  in  a  special  manner. 

Thus,  when  a  company  winds  up  business,  the  final  dis- 
tribution of  the  proceeds  is  not  treated  as  an  ordinary 
dividend;  the  most  of  these  proceeds  are  regarded  as 
capital  returned  to  the  stockholders.  The  "company" 
therefore  goes  through  the  form  of  paying  for  the  shares 
of  its  stockholders  and  enters  what  it  thus  pays  over  to  the 
stockholders  as  a  cost  of  purchase  instead  of  as  a  dividend. 

The  reverse  operations  may  occur  if  at  any  time  the  stock- 
holders forego  their  dividends.  It  is  in  such  a  way  that  a 
company  usually  enlarges  its  capital.  It  nominally  dis- 
tributes the  regular  dividends,  but  allows  the  stockholders 


NATURE   OF   CAPITAL   AND   INCOME        [CHAP.  XV 

who  choose  to  do  so  to  reinvest  them  and  receive  in  return 
new  stock  certificates. 

§6 

From  the  foregoing  accounts  it  is  clear  that  the  theory 
of  capital  and  income  which  has  been  explained  applies 
practically  to  the  accounting  ordinarily  employed  in  busi- 
ness. Such  accounting  is,  in  fact,  nothing  but  a  method  of 
recording  the  items  of  income  and  their  capitalization  at 
different  points  of  time.  A  merchant's  balance  sheet  is  a 
statement  of  the  prospects  of  his  business.  Each  item  in  it 
represents  the  discounted  value  of  items  which  he  may 
expect  later  to  enter  in  his  income  account.  Rightly  in- 
terpreted, the  capital  account  merely  represents  as  a  whole 
the  capitalization  of  expected  items  in  the  income  account; 
the  fluctuations  of  the  capital  account  correspond  with  the 
deviations  from  the  standard  income  in  the  items  of  the  income 
account;  and  where  there  are  no  such  fluctuations,  every 
item  of  the  income  account  is  equal  to  the  standard  income 
from  the  corresponding  items  of  the  capital  account. 

There  are,  of  course,  numerous  practical  modifica- 
tions of  this  general  statement  to  be  made  when  actual 
accounts  are  treated.  It  was  shown  in  Chapter  VIII  that 
such  modifications  are  due  to  a  variety  of  circumstances, 
such,  for  instance,  as  the  influence  of  that  important  ele- 
ment, risk;  the  desire  of  accountants  to  maintain  their 
capital  accounts  unchanged  from  year  to  year;  and  the 
omission  from  their  capital  accounts  of  such  two-sided 
items  as  leases,  employee-contracts,  and  the  like.  But  none 
of  the  exigencies  of  practice  militate  in  the  least  against  our 
theory  of  capital  and  income  accounts.  In  all  cases  the 
income  account  simply  records  the  values  of  the  services 
arid  disservices  of  articles  of  property  through  any  given 
period ;  and  the  capital  account  records  the  present  values 
of  those  articles,  as  resulting  at  any  given  instant  from  the 
expected  values  of  their  services  and  disservices. 


CHAPTER  XVI 

THE   RISK    ELEMENT 
§1 

THROUGHOUT  the  three  previous  chapters,  we  have  as- 
sumed the  existence  of  artificially  simple  conditions.  We 
have  assumed  that  the  entire  future  history  of  the  capital 
in  question  is  definitely  known  in  advance ;  in  other  words, 
we  have  ignored  chance.  The  factory  which  was  taken 
for  illustration  was  supposed  to  yield  definite  future  in- 
come which  could  be  counted  upon  as  a  bondholder  counts 
upon  his  interest.  In  actual  practice,  however,  every  factory 
or  other  enterprise  offers  chances  both  of  gain  and  loss. 
How  these  chances  affect  capital-value  will  be  discussed 
in  the  present  chapter. 

We  have  seen  that  capital-value  increases  as  an  antici- 
pated installment  of  income  approaches  in  time,  and 
diminishes  as  that  installment  is  reached  and  passed.  These 
changes  in  capital-value  take  place  when  the  future  in- 
come is  regarded  as  certain.  The  introduction  of  the 
element  of  chance  will  bring  other  and  even  more  impor- 
tant changes  in  capital-value.  If  we  take  the  history  of 
the  prices  of  stocks  and  bonds,  we  shall  find  it  chiefly  to 
consist  of  a  record  of  changing  estimates  of  futurity,  due 
to  what  is  called  chance,  rather  than  of  a  record  of  the 
foreknown  approach  and  detachment  of  income.  Few,  if 
any,  future  events  are  entirely  free  from  uncertainty.  In 
fact,  property,  by  its  very  definition,  is  simply  the  right  to 
the  chance  of  future  services.  A  mine  owner  takes  his 
chances  as  to  what  the  mine  will  yield;  the  owner  of  an 
orange  plantation  in  Florida  takes  risks  of  winter  frosts; 

265 


266  NATURE    OF    CAPITAL   AND    INCOME       [CHAP.  XVI 

the  owner  of  a  farm  takes  risks  as  to  the  effect  of  sun 
and  rain  and  other  meteorological  conditions,  as  well  as 
risks  of  the  ravages  of  fire,  insects,  and  other  pests.  In 
buying  an  overcoat  a  man  takes  some  risk  as  to  its  effec- 
tiveness in  excluding  cold,  and  as  to  the  length  of  time  it 
will  continue  to  be  serviceable.  Even  what  are  called 
"gilt-edged"  securities  are  not  entirely  free  from  risk.  In 
a  sense,  therefore,  every  owner  of  property  is  a  risk-taker. 
Some  persons  will  estimate  more  highly  than  others  the 
risks  taken.  From  this  fact  it  might  seem  that  there 
is  a  distinction  between  the  actual  risk  incurred  and  the 
estimate  which  individuals  put  upon  it.  But  a  little 
consideration  will  show  that  this  distinction  is  spurious; 
for,  by  the  nature  of  the  case,  chance  is  always  an  estimate. 
Chance  is  subjective.  Although  one  man's  estimate  may 
be  better  than  another's  through  superior  knowledge,  intui- 
tion, or  experience,  the  best  estimate  is  still  only  an  estimate, 
not  a  certainty.  In  the  actual  world  of  events  there  is  no 
uncertainty.  Aside  from  human  opinion,  there  is  no  such 
thing  as  chance.  To  an  omniscient  being,  all  things  are 
certain. 

It  must  be  admitted  that  this  view  of  chance  is  not 
familiar  to  the  ordinary  man,  nor  is  it  universally  accepted 
by  the  professed  students  of  chance.  Thus,  writers  like 
Dr.  Venn,  adhering  to  an  objective  theory,  regard  the  chance 
of  an  event  as  the  number  of  times  it  would  occur  in  the 
long  run,  out  of  the  total  series  of  possible  occurrences.  But 
no  matter  how  long  the  "run,"  the  number  of  times  the 
event  actually  occurs  seldom  corresponds  exactly  with  the 
chance  of  its  occurring.  Even  in  so  simple  a  case  as  coin- 
tossing,  1000  trials  will  not  often  give  exactly  500  heads 
and  500  tails.  Yet  even  the  "long-run"  theorists  regard 
the  chances  of  heads  and  tails  as  even.  If  600  heads  fa.! 
and  only  400  tails,  the  odds  are  not  6  to  4.  To  this  objec- 
tion the  only  answer  offered  by  the  long-run  theorists  is 
that  the  run  is  not  long  enough,  that  heads  and  tails  are 


SEC.  1]  THE    RISK    ELEMENT  267 

equally  probable  because  the  longer  the  trial  is  continued 
the  more  will  the  two  tend  toward  equality.  But  they 
argue  in  a  circle.  It  is  not  necessarily  true  that  the 
longer  the  run  the  more  closely  will  the  frequency  of  the 
event  approach  its  probability.  For  example,  it  is  possible 
that  though  heads  and  tails  have  an  equal  chance,  a  run 
of  heads  may  keep  up  for  any  given  number  of  times, 
however  long,  a  million,  for  instance;  or  that  at  first  heads 
and  tails  may  occur  with  equal  frequency  and  as  the  ex- 
periment proceeds  they  may  diverge  more  and  more  from 
such  equality.  No  student  of  chance,  whatever  his  theory 
of  the  philosophy  of  chance,  would  claim  that  these  cases 
are  impossible.  The  most  that  can  be  said  is  that  they  are 
extremely  improbable.  The  statement,  therefore,  that  the 
longer  the  run  the  more  closely  will  the  frequency  of  the 
event  approach  its  probability  turns  out  to  be  "the  longer 
the  run  the  more  probably  will  the  frequency  correspond 
to  the  probability."  This  is  true  as  a  proposition  and  it  is 
in  fact  known  as  " Bernoulli's  Theorem";  but  it  cannot 
be  made  the  basis  of  a  sound  definition  of  probability,  for 
probability  would  be  defined  in  terms  of  itself.  It  states 
that  the  probability  of  heads  coming  up  is  the  frequency 
which  heads  will  probably  approximate  in  the  long  run ! 
How  else  than  in  terms  of  probability  can  we  formulate 
the  conditions  under  which  in  the  long  run  the  coin 
"will"  fall  according  to  its  probability?  It  is  precisely 
at  this  point  that  the  radical  difficulty  with  the  "long- 
run  "  theory  is  seen.  It  is  said  that  in  an  athletic  contest, 
the  chance  of  winning  is  one  half  when  two  wrestlers  are 
so  nearly  mated  that  in  the  long  run  "under  precisely  the 
same  conditions/'  each  will  win  in  half  the  contests.  If 
the  conditions  are,  literally  speaking,  precisely  the  same, 
then  the  same  result  will  necessarily  follow  and  the  same 
man  will  always  win.  It  is  only  as  the  conditions  vary 
slightly  from  time  to  time  in  their  unknown  elements  that 
there  is  a  change  of  winner;  and  the  instant  the  unknown- 


268  NATURE    OF   CAPITAL   AND   INCOME       [CHAP.  XVI 

ness  of  these  elements  is  introduced  into  the  problem,  the 
observer  unconsciously  shifts  his  ground  from  the  "  long 
run  "  to  the  true  theory  of  chance. 

Chance  is,  then,  an  affair  of  human  knowledge  or  igno- 
rance. According  to  this  —  the  ignorance  —  theory,  chance 
is  not  objective,  but  subjective.  Outside  of  the  mind, 
chance  has  no  place.  If  a  man  holds  a  coin  in  his  hand  and, 
without  letting  it  be  seen,  asks  his  neighbor  what  the 
"real"  chance  is  that  heads  are  up,  will  not  the  latter  reply 
one  half?  But  as  a  matter  of  fact  the  position  of  the  coin 
is  absolutely  determinate.  Either  heads  are  up,  or  tails 
are  up;  there  is  no  ambiguity.  Without  changing  the 
coin,  the  holder  opens  his  hand.  He  sees  that  heads  are 
up.  Without  disclosing  this  fact  to  his  neighbor  he  re- 
peats the  question,  "What  is  the  chance  that  heads  are 
up?"  Will  not  the  latter  still  reply,  "One  half"?  To 
him,  in  his  ignorance  about  the  coin,  the  chances  are 
exactly  even;  but  to  the  man  who  holds  the  coin  and 
whose  eye  has  seen  it,  there  is  no  uncertainty.  He  knows 
that  heads  are  up.  For  him  the  element  of  chance  has 
vanished  because  the  element  of  ignorance  has  vanished. 
Chance  exists  only  so  far  as  ignorance  exists ;  varies  with 
different  persons  according  to  their  comparative  ignorance 
of  the  matter  under  consideration ;  and  is  in  fact  a  measure 
of  ignorance. 

Of  course  the  actual  statistical  record  may  afford  an  im- 
portant and  sometimes  the  only  basis  for  our  degree  of 
knowledge  and  ignorance.  Practically  it  therefore  often 
happens  that  we  derive  our  estimate  of  chances  from  the 
behavior  of  events  "in  the  long  run."  It  is  thus  that  the 
chances  of  fire,  shipwreck,  and  death  are  estimated  by  the 
insurance  companies.  But  while  statistics  supply  data 
for  the  forming  of  subjective  estimates  of  chances,  they  do 
not,  themselves,  constitute  chances;  and  even  when  they 
enter  into  the  problem  the  insurance  examiner  does  not 
follow  them  blindly.  He  always  examines  the  special 


SEC.  2]  THE   RISK    ELEMENT  269 

circumstances  of  each  case;  and  his  final  estimate  of  the 
chance  that  a  particular  building  will  burn,  a  particular 
ship  founder,  or  a  particular  person  die,  is  based  on  all  the 
data  available,  among  which  the  data  supplied  by  statis- 
tics are  an  important  but  by  no  means  the  sole  element. 

To  apply  this  idea  of  chance  to  an  economic  example, 
consider  a  gold  mine.  What  is  the  chance  that  it  conceals 
a  rich  lead  of  ore?  The  ordinary  man  makes  an  estimate, 
based  on  his  experience  or  inexperience.  The  geologist 
has  additional  knowledge  and  would  make  a  different  esti- 
mate. In  actual  fact,  however,  gold  is  either  actually 
there  in  certain  definite  quantities,  or  is  totally  absent. 
It  is  a  coin  held  in  nature's  closed  hand. 

§2 

But,  in  showing  that  chance  is  purely  a  psychological 
and  not  an  objective  magnitude,  we  are  still  far  from  de- 
fining chance  as  a  mathematical  magnitude.  In  order  to 
measure  chance,  it  is  necessary  to  state  (1)  when  two 
chances  are  equal  or  unequal;  and  (2)  when  one  chance 
bears  any  given  ratio  to  the  other. 

The  chance  of  one  event  is  said  to  be  equal  to  the  chance 
of  another  in  the  mind  of  a  particular  individual,  when  that 
individual  has  no  inclination  to  believe  that  one  will  occur 
rather  than  the  other.  One  of  the  chances  is  said  to  exceed 
the  other  when  the  individual  is  "inclined  to  believe" 
that  one  event  will  occur  rather  than  the  other.  The  test 
of  the  equality  of  two  chances  is  mere  indecision  of  opinion 
—  opinion  exactly  and  evenly  balanced. 

Next  comes  the  question  of  the  ratio  of  twro  chances. 
When  it  is  said  that  the  odds  in  favor  of  one  event  as 
compared  with  another  are  two  to  one,  the  meaning  is 
that  out  of  three  equally  probable  combinations  of  condi- 
tions, two  imply  the  first  event  and  only  one  the  second. 
Thus,  if  there  are  three  cards  in  a  hat,  of  which  it  is 
known  that  only  one  will  draw  a  prize,  the  chance  against 


270  NATURE    OF    CAPITAL   AND    INCOME      [CHAP.  XVI 

a  person  who  draws  a  card  from  the  hat  receiving  the  prize 
is  two  to  one;  for  of  the  three  equally  probable  drawings, 
two  are  blanks. 

In  general  terms  the  odds  in  favor  of  one  event  as  com- 
pared with  another  are  said  to  be  m  to  n  when  there  are 
m  +  n  equally  probable  cases  in  which  one  or  the  other  of 
the  two  events  may  happen,  and  among  these  m  +  n  cases 
there  are  m  cases  such  that  the  first  event  would  happen, 
and  n  cases  such  that  the  second  event  would  happen. 
The  chance  of  the  first  event  is  then  ~  and  the  chance  of 
the  second  is  ~.  The  m  and  the  n  cases  are,  it  should 
be  noted,  assumed  to  be  mutually  exclusive.1 

Probability  is  thus  not  merely  an  affair  of  pure  mathe- 
matics, as  is  so  often  imagined.  It  is,  first  of  all,  a  matter 
of  concrete  human  estimate.  What  are  called  the  mathe- 
matics of  probability  apply  only  to  arrays  of  equally  prob- 
able combinations,  and  consist  in  calculating  the  number  of 
these  which  are  favorable  or  unfavorable  to  a  given  event. 
The  mathematics  of  probability  never  establish  a  prob- 
ability of  itself,  but  always  rest  on  some  human  estimate 
of  chances  which  are  equal  to  start  with.  Like  every  other 
branch  of  applied  mathematics,  it  must  depend  on  having 
its  raw  material  supplied  from  without.  By  mathematics 
we  seem  to  discover  that  the  chance  of  throwing  double 
sixes  with  two  dice  is  one  in  thirty-six.  But  this  calcula- 
tion rests  on  the  hypothesis  that,  in  some  person's  esti- 
mation, each  die  is  equally  liable  to  fall  on  any  one  of 
its  six  faces.  Starting  with  this  assumption,  it  is  easy  to 
show  that  in  throwing  two  dice  there  are  thirty-six  equally 

1  It  often  happens  that  we  cannot  divide  the  field  of  probability 
into  separate  cases  all  equally  probable.  In  such  a  case  the  mind  is 
forced  to  make  an  estimate.  For  instance,  the  probability  of  an 
event  may  be  said  to  be  one  third  against  the  field  if  the  estimator's 
state  of  opinion  toward  the  field  is  exactly  similar  to  his  state  of 
mind  toward  another  field  in  which  the  division  into  three  separate 
combinations  is  possible  and  one  of  them  favors  the  event  in  ques- 
tion. If  the  state  of  mind  is  similar  but  less  definite,  then  the  chance 
is  "  about  "  one  third  but  uot  definite. 


SEC.  3]  THE    RISK    ELEMENT  271 

probable  cases  and  that  only  one  of  these  will  give  double 
sixes.  Mathematics  could  not  obtain  the  result  unaided 
by  experience.  All  that  mathematics  accomplished  with 
the  dice  was  to  derive  a  result  from  the  assumed  con- 
ditions of  two  sets  of  six  equal  chances.  Whether  these 
assumed  conditions  existed  was  a  question,  not  of  mathe- 
matics, but  of  concrete  opinion.  If  the  dice  were  known  to 
be  "loaded,"  the  case  would  be  materially  altered. 


In  order  to  apply  this  theory  of  chance  to  the  valuation 
of  capital,  we  observe  that  both  the  future  rate  of  interest 
and  the  future  items  of  income  are  uncertain.  In  the  prob- 
lem of  capital-valuation,  however,  the  uncertainty  in  the 
rate  of  interest  does  not  always  enter,  for  only  present 
and  not  future  rates  are  employed  at  the  time  at  which 
the  valuation  of  the  capital  is  made.  When  we  call  a  rate 
a  "  present "  rate  we  mean,  of  course,  that  the  contract 
or  estimate  to  which  it  relates  is  a  present  contract  or 
estimate.  The  very  fact  of  valuation  implies  a  known 
rate  or  rates  at  which  the  valuer  is  contrasting  present 
and  future  goods.  There  may  be  several  "  present  "  rates. 
Thus  if  the  "  present  "  be  the  year  1906.  we  may  imagine 
a  whole  series  of  rates  of  interest  holding  true  in  1906  for 
such  a  man;  for  instance,  4  per  cent  for  a  1-year  contract, 
6  per  cent  for  a  5-year  contract,  and  5  per  cent  for  a  15- 
year  contract,  all  originating  at  the  present  moment.  All 
of  these  rates  are  fixed  and  known  and  hold  true  in  the 
year  1906,  but  they  do  not  determine  the  rates  which 
will  hold  true  for  the  contracts  or  estimates  of  1907  or 
1914. 

In  valuing  capital,  therefore,  it  is  not  necessary  to  regard 
the  rate  of  interest  as  uncertain  except  when  the  rate  in 
question  is  a  future  rate. 

Let  us  suppose  that  in  Figure  10  the  income  AB  is 
due  at  the  end  of  the  time  FA,  and  that  the  rate  of  interest 


272 


NATURE   OF   CAPITAL   AND    INCOME      [CHAP.  XVI 


is  such  as  to  produce  the  discount  curve  BE.  Then  the  pres- 
ent value  of  AB  is  FE.  But  the  future  valuations  of  AB 
may  not  follow  the  line  EB  as  they  would  were  the  rate 
of  interest  unchanged.  Thus,  at  a  midway  point  of  time, 
G,  the  valuation  of  AB  may  be  only  GD,  found  by  means  of 
a  higher  rate  of  interest  involving  the  steeper  discount  curve 
DB.  The  history  of  the  value  of  the  property,  namely, 
the  right  to  AB,  therefore  follows  the  broken  line  ECDB} 
abruptly  changing  from  GC  to  GD,  if  we  suppose  G  to  be 


F  G 

FIG.  10. 

the  point  at  which  the  rate  of  interest  changes  unexpectedly 
from  one  level  to  the  other.  Had  the  owner  of  the  property 
foreseen  at  the  start  that  when  the  point  G  was  reached 
the  rate  of  interest  would  be  higher,  he  would  have  taken 
this  fact  into  account  in  valuing  the  property  at  the  moment 
F,  and  the  value  would  have  been  FEf,  found  by  using  the 
discount  curve  BDE'.  This  curve  has  a  slight  angle  at  D, 
being  composed  of  the  curve  BD,  constructed  according  to 
the  high  rate  of  interest  prevailing  at  the  time  G,  and  the 
curve  DE,'  constructed  according  to  the  lower  rate  of  in- 
terest which  applies  to  the  period  FG  and  which  was  em- 
ployed in  the  curve  EC.  The  essential  fact,  therefore,  is 
that  because  of  the  failure  to  foresee  the  future  rise  in  the 


SEC.  4]  THE    RISK    ELEMENT  273 

rate  of  interest,  the  value  of  the  property  is  FE,  instead  of 
FE' ,  and  that  the  value  of  the  capital  will  fall,  as  at  CD, 
or  it  may  be  rise,  in  accordance  with  successive  future  ad- 
justments in  the  rate  of  interest.  Since  these  readjust- 
ments are  usually  small  and  gradual,  fluctuations  in  the 
capital-value  will  not  ordinarily  be  as  great  or  as  abrupt 
as  here  represented,  but  the  principle  involved  will  still 
hold  true.  We  see,  therefore,  a  new  cause  for  the 
fluctuations  in  capital-value,  namely,  unforeseen  changes 
in  the  rate  of  interest. 

§4 

There  is,  however,  a  more  fundamental  way  in  which  a 
change  in  the  rate  of  interest  enters  into  our  calculations, 
for  it  will  affect  the  magnitude  of  the  future  income  items 
themselves.  In  the  above  example  it  was  assumed  that 
the  income  items  were  not  dependent  on  the  rate  of  interest. 
But  it  often  happens  that  the  income  items  are  not  elements 
of  what  in  Chapter  VIII  we  called  "final  income,"  but  are 
"interactions";  or,  in  more  practical  language,  it  often 
happens  that  the  income  is  to  be  reinvested.  In  this  case 
such  an  item  cancels  itself  out  and  leaves  in  its  place  a 
series  of  income  items  in  the  future,  and  the  magnitude  of 
the  income  items  in  this  later  series  will  depend  on  the  rate 
of  interest  at  which  the  preliminary  "interaction"  was  re- 
invested. If  the  intention  in  advance  is  to  reinvest,  it 
becomes  important  not  simply  to  know  the  present  rate 
of  interest,  but  to  forecast  the  future  rate.  This  enters 
into  the  calculations  of  an  investor  who  holds  a  25-year 
bond  at  5  per  cent.  He  will  usually  regard  the  final  pay- 
ment as  "principal,"  intending  that  when  it  becomes  due 
it  shall  be  reinvested  in  a  similar  25-year  bond.  He,  there- 
fore, is  not  really  buying  a  25-year  income  stream  of  $5 
a  year  plus  S100  at  the  end  of  the  term,  but  is  buying,  let 
us  say,  a  50-year  income  stream  consisting  of  $5  per  year 
for  the  first  25  years  and  an  unknown  amount  per  year  dur- 


274  NATURE    OF   CAPITAL   AND   INCOME      [CHAP.  XVI 

ing  the  second  25  years.  In  order  to  forecast  what  income 
will  be  received  in  the  second  period,  he  has  to  forecast 
the  rate  of  interest.  In  other  words,  although  the  bond  repre- 
sents nominally  a  fixed  and  certain  series  of  income  items, 
yet,  in  view  of  the  intention  to  reinvest,  it  actually  repre- 
sents an  income  which  is  quite  uncertain  after  25  years, 
because  of  the  uncertainty  in  the  future  rate  of  interest. 
Such  an  investor,  if  he  expected  the  rate  of  interest  at  the 
end  of  25  years  to  be  2  per  cent,  would,  in  purchasing  the 
above-mentioned  bond,  be  getting  $5  a  year  for  25  years 
and  $2  a  year  for  the  next  25  years.  Under  these  condi- 
tions, if  he  could  buy  a  50-year  bond  at  4  per  cent,  he  would 
prefer  to  do  so.  But,  if  he  expected  the  rate  of  interest  to 
remain,  for  each  25-year  period,  at  5  per  cent,  he  would  pre- 
fer, rather  than  invest  now  in  a  50-year  bond  at  4  per  cent, 
to  invest  in  the  25-year  bond  at  5  per  cent,  intending  to 
reinvest  at  5  per  cent  at  the  expiration  of  the  term.  His 
forecast  of  what  the  rate  of  interest  will  be  in  25  years  will 
thus  materially  affect  the  choice  of  his  investments  to-day. 
Those  who  expect  the  rate  of  interest  to  fall  will  prefer  to 
invest  in  long-time  securities  at  the  present  market  rates, 
even  when  those  rates  are  less  than  on  securities  of  shorter 
time,  while  those  who  expect  the  rate  of  interest  to  rise  will 
prefer  short-time  securities.  In  the  case  of  insurance  com- 
panies which  are  constantly  reinvesting,  a  change  in  the 
rate  of  interest  becomes  a  very  serious  matter.  One  of 
the  actuaries  of  a  large  company  has  recently  pointed  out 
that  such  changes  in  the  rate  of  interest  are  not  uncommonly 
encountered  and  are  more  important  for  the  prosperity 
of  the  company  than  the  most  unusual  changes  in  the  mor- 
tality tables.  Insurance  companies  can  only  roughly  take 
account  of  the  chances,  reckoning  that  the  greater  the 
likelihood  of  a  rise,  the  better  the  policy  of  making  tem- 
porary investments  at  high  rates;  and  the  greater  the 
likelihood  of  a  fall,  the  better  the  policy  of  making 
permanent  investments,  even  at  moderately  low  rates. 


SEC.  6]  THE   RISK   ELEMENT  275 

§5 

The  main  application  of  risk  to  capital  valuation  is, 
however,  not  to  the  rate  of  interest,  but  to  the  income 
items  themselves.  To  this  application  we  now  address 
ourselves.  Let  us  begin  by  considering  the  case  in  which 
the  element  of  discounting  is  wholly  absent.  The  simplest 
case  is  that  of  ordinary  gambling.  If  one  invests  in  a 
lottery  ticket  where  there  is  one  chance  in  ten  of  drawing 
a  prize  of  S50,  it  is  evident  that  the  price  of  the  ticket 
must  be  considerably  less  than  $50,  which  is  the  income 
it  may  yield.  Mathematicians  have  called  the  product 
of  the  prize  multiplied  by  its  probability,  the  "math- 
ematical value"  of  the  chance.  In  the  present  instance 
this  "mathematical  value"  will  be  $50  x  J-Q,  or  $5. 
If  a  professional  gambler  should  always  pay  the  mathe- 
matical value  of  the  chances,  he  would,  in  the  long  run, 
probably  come  out  about  even,  as  is  well  known  from 
"Bernoulli's  Theorem."  Thus,  if  he  continued  to  try  for 
such  $50  prizes,  paying  each  time  $5,  he  would  probably 
win  about  one  time  in  ten.  In  a  thousand  trials,  there- 
fore, he  might  expect  to  win  100  times,  spending  $5  each 
for  his  1000  tickets,  or  $5000,  and  receiving  $50  each  for 
his  100  prizes,  or  $5000. 

But  the  actual  price  which  one  will  pay  is  not  necessarily 
the  mathematical  value  of  the  chance.  It  may  be  higher  ; 
it  is  usually  lower.  The  gambler  is  usually  a  person  who 
will  pay  more  than  the  mathematical  value  of  the  chance. 
At  Monte  Carlo,  the  "bank"  makes  its  profit  in  this  way, 
although  its  victims  know  full  well  that  they  are  paying 
more  than  the  mathematical  value  of  their  chances.  The 
consequence,  of  course,  is  ruin  to  most  of  them.  Fortu- 
nately, persons  who  deliberately  gamble  are  in  most  com- 
munities in  the  minority.  The  ordinary  man  is  unwilling 
to  pay  even  the  full  mathematical  value  of  the  chance. 
He  is  reluctant  to  assume  any  risks,  and  is,  on  the 


276  NATURE   OF   CAPITAL   AND    INCOME      [CiiAP.  XVI 

contrary,  willing  to  make  sacrifices  in  order  to  rid  himself 
of  them.  Where  the  gambler  would  be  willing  to  pay  more 
than  So  for  his  lottery  tickets,  the  cautious  investor  would 
only  .be  induced  to  buy  such  tickets  for  considerably  less 
than  So.  To  him,  the  chance  of  gain  is  outweighed  by  the 
prospect  of  loss.  Rather  than  risk  little  in  order  to  obtain 
large  gains,  he  prefers  to  sacrifice  much  in  order  to  avoid 
large  losses.  It  is  this  sentiment  which  gives  rise  to 
the  phenomenon  of  insurance. 

§6 

There  are  three  values  which  apply  to  an  uncertain 
return :  (1)  the  value  which  that  return  would  have  if  the 
uncertainty  could  be  eliminated,  or  its  riskless  value; 
(2)  the  value  which  would  be  attached  to  it  if  the  investor 
were  willing  to  pay  the  product  of  the  income  by  the  chance 
of  obtaining  it,  or  the  mathematical  value ;  (3)  the  value 
which  he  is  actually  willing  to  pay,  or  the  commercial  value. 
Thus  in  the  case  of  the  lottery  ticket,  entitling  the 
holder  to  the  chance  of  $100,  the  riskless  value  is 
$100;  the  mathematical  value  is  $5;  and  the  commer- 
cial value,  more  than  $5  for  the  reckless,  less  for  the 
man  of  ordinary  caution,  and  just  $5  for  those  of  an 
intermediate  temperament. 

The  ratio  of  the  mathematical  to  the  riskless  value  may 
be  called  the  "  coefficient  of  probability."  In  the  supposed 
case  of  the  lottery  ticket  this  coefficient  is  -jf  Q-.  The  ratio 
of  the  commercial  to  the  mathematical  value  —  a  ratio 
which  will  vary  according  to  the  temperament  of  the  in- 
dividual—  may  be  called  the  "  coefficient  of  caution." 
In  the  case  of  a  man  who  values  his  chance  at  $4,  this  coeffi- 
cient would  be  -|.  Given  these  ratios,  we  can  for  a  given 
individual  derive  the  commercial  value  from  the  riskless 
value  by  multiplying  the  riskless  value  by  the  coefficient 
of  probability  and  the  result  by  the  coefficient  of  caution, 
thus  :  $  100  x  I^-Q  x  -f  =  $4.  The  product  of  these  two  ratios 


SEC.  7]  ,  THF,    RISK    ELEMENT  277 

is  the  ratio  of  the  commercial  to  the  riskless  value 
(-j$jy  x  |=  -i^)  and  may  be  called  the  coefficient  of  ri*k.1 
The  coefficient  of  caution  expresses  a  feature  of  individ- 
ual character  as  determined  partly  by  nature  and  partly 
by  environment.  In  times  like  the  colonial  period  when 
lotteries  were  common,  or  in  places  like  Monte  Carlo,  where 
gamblers  congregate,  the  coefficient  of  caution  is  such  as  to 
represent  an  abnormal  lack  of  caution.  The  opposite 
extreme  is  found  in  the  timid  investor  who  hoards  money 
rather  than  risk  its  investment  in  any  form.  The  coefficient 
of  caution  also  varies  with  the  same  individual  under 
different  circumstances.  Chief  among  these  varying  cir- 
cumstances, as  Professor  Norton  has  pointed  out,  is  the 
amount  of  capital  of  which  the  individual  is  possessed. 
The  more  capital  a  man  possesses,  the  less  is  his  chance 
of  serious  loss  in  any  enterprise  involving  risk ;  and  for  this 
reason  a  rich  man  finds  it  possible  to  grow  still  richer. 
The  rich  can  well  afford  to  lose  millions  where  the  poor 
could  barely  afford  to  lose  hundreds.  There  is  less  likeli- 
hood of  ruin  to  the  United  States  Steel  Corporation  from  its 
projected  investment  of  $75,000,000  to  found  a  new  steel- 
producing  city  than  there  would  be  to  a  workingman 
who  makes  a  "  safe  "  investment  of  $1000. 

§7 

We  are  now  in  a  position  to  apply  these  principles  of 
probability  to  the  valuation  of  capital,  i.e.  to  the  capitaliza- 
tion of  uncertain  income.  The  most  important  classifica- 
tion of  investments  from  a  practical  point  of  view  is  into 
two  categories  of  safe  and  unsafe  investments.  But  even 
in  so-called  safe  investments  the  element  of  risk  enters. 
As  between  bonds  and  stocks,  the  latter  usually  represent 
the  precarious  and  the  former  the  safe  investments;  yet 
in  the  case  of  bonds,  the  receipt  of  interest  and  principal 
is  always  in  some  degree  a  matter  of  uncertainty. 

1  For  a  mathematical  statement,  see  Appendix  to  Chap.  XVI,  §  1. 


278  NATURE    OF    CAPITAL   AND    INCOME      [CHAP.  XVI 

Take,  for  example,  a  "5  per  cent"  bond  running  for 
10  years.  Let  us  assume  that  the  market  rate  of  interest 
is  4  per  cent,  in  the  sense  that  $100  at  any  time  will  exchange 
for  8104  certain  one  year  later.  Under  these  conditions, 
the  bond  ought  to  sell  for  $108  (see  Chapter  XIII).  That 
is,  an  investor  buying  this  bond  at  a  premium  of  $8  will 
in  10  years  "make"  4  per  cent  provided  he  receives  all 
the  sums  stipulated.  The  $108  is  the  "riskless  value" 
of  the  bond. 

But,  while  $108  would  be  the  price  of  the  bond  were  the 
investor  absolutely  sure  of  the  income  items  to  which  it 
entitles  him,  he  may  feel  that  there  is  a  risk,  —  for 
instance,  that  the  probability  of  any  given  interest 
payment  is  only  -£-$,  in  which  event  it  is  evident  that  he 
will  not  pay  $108.  We  can  easily  calculate,  on  the 
basis  of  the  assumed  probability,  that  what  has  been 
called  the  " mathematical  value"  of  the  bond  would  be 
$97.  This  figure  is  found  by  multiplying  each  income 
item  by  its  coefficient  of  probability  and  discounting 
the  result  at  the  market  rate  of  interest,  4  per  cent. 
We  assume  here  that  the  risk  attached  to  each  indi- 
vidual interest  and  principal  payment  is  independent  of 
that  attached  to  all  the  others.  The  probability  of  receiv- 
ing each  payment  is  -^Q  ,  and  the  risk  of  its  not  being  received 
is  in  each  case  -^ .  It  is  evident  that  the  first  payment  of  $5, 
due  in  one  year,  has  at  that  time  a  mathematical  value  of 
5  x  -j9Q ,  and  the  present  value,  when  discounted  at  4  per  cent, 
would  be  '~(lf  -  If  the  same  expressions  be  obtained  for  all 
the  other  items  of  income,  and  the  sum  total  of  the  present 
valuations  be  found,  it  is  evident  that  in  the  result  the  factor 
-j9f7  will  appear  for  every  individual  sum,  and  that  the  total 
will  simply  be  -fy  as  much  as  though  the  element  of  risk  were 
absent.  In  other  words,  the  "mathematical  value"  of 
the  bond  will  be  -^  of  its  riskless  value  of  $108,  or  about 
$97. 

Hut    the   actual   " commercial  value"  of  the  bond  will 


SEC.  8]  THK    RISK    ELEMENT  279 

ordinarily  be  less  than  this  "mathematical  value"  of  $97. 
We  may  suppose  it  to  be  $92.50,  indicating  a  coefficient  of 
caution  of  -^f-  •  Here,  as  in  the  case  of  the  lottery  ticket, 
we  have  regarded  the  actual  value  of  the  bond  as  obtained 
from  its  riskless  value  by  applying  first  the  probability 
factor,  and  second  the  caution  factor,  9y7-. 

If  the  probabilities  of  receiving  the  individual  interest 
payments  were  not  regarded  as  independent,  the  calcula- 
tions of  the  mathematical  value  would  differ  somewhat 
from  the  preceding.  Thus,  if  we  suppose  that  default  in 
one  interest  payment  carried  with  it,  by  the  terms  of  the 
contract,  the  default  in  all  subsequent  interest  payments, 
we  should  have  to  apply  the  theory  of  probability  some- 
what differently1  but  the  principle  would  be  the  same. 

§8 

There  is  another  way,  and  one  which  conforms  more  to 
ordinary  usage,  in  which  the  commercial  value  of  the  bond 
may  be  derived  from  the  riskless  value.  While  the  price  of 
the  bond  will  vary  inversely  with  the  risk,  the  rate  of 
interest  varies  directly  with  the  risk ;  so  that  as  the  value 
of  the  bond  descends,  the  corresponding  rate  of  interest 
will  ascend.  Thus  we  have  riskless,  mathematical,  and 
commercial  rates  of  interest  —  4  per  cent,  5.4  per  cent,  and 
6  per  cent  —  corresponding  respectively  with  the  riskless, 
mathematical,  and  commercial  values  of  the  bond  —  S108, 
$97,  $92.50. 

The  question  sometimes  arises,  where  the  element  of 
risk  thus  raises  the  basis  on  which  the  bond  is  sold,  whether 
the  6  per  cent  is  a  true  "rate  of  interest."  The  ques- 
tion is  purely  one  of  definition.  Were  it  possible,  it  would 
be  simpler  to  confine  the  application  of  the  phrase  "  rate  of 
interest"  to  an  exchange  between  present  and  future  risk- 
less  income.  But  in  this  case,  it  is  always  exceedingly  diffi- 

1  For  the  consideration  of  this  case,  see  Appendix  to  Chap.  XVI,  §  2. 


280  NATURE    OF   CAPITAL   AND   INCOME      [CnAP.  XVI 

cult  to  state  what  the  riskless  rate  of  interest  is,  since  some 
slight  risk  attaches  to  almost  every  investment.  Accord- 
ingly it  is  usual  to  regard  the  commercial  rate  as  a  true 
"rate  of  interest."  The  best  course,  therefore,  is  to  recog- 
nize all  three  as  rates  of  interest,  distinguishing  them, 
when  necessary,  as  "  riskless/'  "mathematical,"  and 
"commercial." 

§9 

When  we  speak  of  the  riskless  value  or  the  riskless  rate, 
we  intend  by  the  employment  of  the  word  "riskless/' 
to  exclude  from  consideration  the  chance  element  entirely 
—  not  only  the  risk  of  receiving  less,  but  also  the  chance  of 
receiving  more  than  the  specified  income.  For  cases  are 
not  wanting  in  which  the  mathematical  and  commercial 
values  of  a  security  are,  by  reason  of  the  chance  that  it 
will  prove  extra-profitable,  more  than  its  riskless  value. 
Take,  for  instance,  a  $100  share  of  preferred  stock,  on 
which  a  minimum  income  of  5  per  cent,  or  $5,  is  assured. 
If  the  true  rate  of  interest  be  4  per  cent,  the  value  of  such 
stock  should  be  $125.  This  is  the  "riskless"  value.  The 
mathematical  value,  however,  will  be  greater,  say  $150, 
inasmuch  as  there  is  a  probability  that  the  holder  will 
receive  more  than  $5  a  year,  and  practically  no  prob- 
ability that  he  will  receive  less.  And  the  commercial  value 
will  be  still  different,  falling,  by  reason  of  the  caution  of 
the  investor,  somewhat  below  the  mathematical,  say  to 
$130. 

Another  instance  is  that  of  United  States  government 
bonds.  The  national  banks  which  invest  in  these  receive, 
besides  the  interest,  a  special  privilege  in  the  form  of  per- 
mission to  issue  bank  notes.  This  additional  benefit  may 
be  regarded  as  a  speciesof  additional  income,  and  materially 
enhances  the  value  of  the  bonds.  For  this  reason, 
United  States  government  bonds  are  not  used  for 
investment  purposes,  except  among  those  in  whom  the  ele- 


SEC.  10]  THE    RISK    ELEMENT  281 

ment  of  caution  is  unduly  strong,  but  are  hold  for  the 
most  part  by  national  banks.  It  is  therefore  misleading 
to  cite,  as  some  have  done,  the  rates  of  interest  realized 
on  government  bonds  as  an  indication  of  the  true  rate  of 
interest.  A  similar  benefit  attaches  to  the  bonds  of  the 
Credit  Foncier  in  France.  These  are  sold  on  a  very  low 
"  basis "  because  of  the  chance,  connected  with  them,  of 
winning  prizes. 

§  10 

In  the  general  case  we  have  to  do  not  simply  with  the 
risk  of  falling  below  a  specified  income,  nor  with  the 
chance  of  rising  above  a  specified  income,  but  with  both. 
Thus,  the  dividends  from  common  stock  have  no  fixed 
minimum  as  do  those  from  good  preferred  stock,  nor  any 
fixed  maximum  as  do  the  interest  payments  from  bonds. 
They  may  vary,  and  vary  widely,  in  either  direction.  The 
amount  of  variation  may  be  measured  with  reference  to  any 
specified  amount  selected  arbitrarily  as  a  basis  of  com- 
parison. For  instance,  in  the  case  of  stock  which  has 
yielded,  in  successive  years,  the  following  percentages: 
5,  5,  6,  5,  5,  4,  5,  7,  5,  3,  4,  5,  we  may  for  conven- 
ience take  5  per  cent  to  serve  for  a  basis  of  computa- 
tion. The  stock  has  yielded  1  per  cent  or  more  in  excess 
of  this  in  two  cases  out  of  twelve ;  it  has  yielded  2  per  cent 
in  excess  in  one  case  out  of  twelve;  it  has  fallen  short  by 
1  per  cent  or  more  in  three  cases  out  of  twelve,  and  fallen 
short  by  2  per  cent  in  one  case  out  of  twelve.  If  these  fre- 
quencies are  our  only  guide  for  judging  the  future,  they 
represent  the  probabilities  of  receiving  the  respective  divi- 
dends. 

On  the  basis  of  the  foregoing  figures  it  is  possible  to  calcu- 
late the  "riskless"  and  the  "mathematical"  value  of  the 
stock,  and,  if  we  know  the  caution  factor,  it  is  possible  to 
calculate  the  "commercial"  value  also.  Thus,  the  "risk- 
less"  value,  in  this  case,  signifies  that  value  which  the  stock 


282  NATURE    OF   CAPITAL   AND    INCOME      [CHAP.  XVI 

would  have  if  it  were  certain  to  yield  the  (arbitrarily 
assumed)  5  per  cent  forever  —  never  more  and  never  less. 
The  riskless  value  is  therefore  simply  the  capitalized  value 
of  a  perpetual  annuity  of  $5  per  share  of  $100  face  value. 
If  the  rate  of  interest  is  4  per  cent,  the  result  is  $5  divided 
by  4  per  cent,  or  $125. 

To  obtain  the  "mathematical"  value  we  simply  add  to 
the  riskless  value  the  value  of  the  chance  of  getting  more, 
and  subtract  that  of  the  chance  of  getting  less.  The 
chance  of  getting  an  additional  $1  a  year  is  found  by  expe- 
rience, as  set  forth  above,  to  be  two  in  twelve,  or  ^  each 
year.  The  present  value  of  the  right  to  this  chance  has 
therefore  a  mathematical  value  ^  as  great  as  though  the  $1 
increment  were  a  certainty.  But  the  certainty  of  $1  a 
year  would  be  worth  $25.  Hence  a  chance  of  1  in  6  of 
getting  $1  a  year  would  be  worth  mathematically  ^  of  $25, 
or  $4.16f.  In  like  manner  the  chance  of  a  second  addi- 
tional dollar  is  one  in  twelve  and  is  worth  (mathematically) 
TV  of  $25,  or  $2.08^.  These  two  terms,  $4.16f  and  $2.08J, 
are  the  additive  terms  sought.  The  subtractive  terms  are 
the  mathematical  value  of  the  chance  of  getting  $1  less 
than  the  $5,  and  of  getting  still  another  $1  less.  These 
chances,  being  3  in  12  and  1  in  12  respectively,  are  worth 
fo  of  $25  and  -jV  of  $25  respectively,  or  $6.25  and  $2.08J. 
The  whole  mathematical  value  is  therefore  $125+  ($4.16§  + 
$2.081) -($6.25 4- $2.08^),  or  $122.91|.  Applying  to  this 
the  factor  of  caution,  which,  let  us  say,  is  ^,  we  find  the 
commercial  value  to  be  $110.63.  The  three  values  are 
thus,  approximately :  — 

"  riskless  "  value $125 

"  mathematical"  value $123 

"  commercial "  value $111 

In  this  manner  we  may  compute  the  three  values  in  any 
other  case.  Usually,  however,  the  chances  involved  are  so 
indefinite  that  the  reckoning  is  made  only  by  rule  of  thumb. 


SEC.  11]  THK    RISK    ELEMENT  283 

Any  further  attempt  to  apply  the  theory  of   probability 
would  therefore  outrun  the  exigencies  of  practice.1 

§11 

The  practical  investor,  in  order  to  estimate  the  influence 
of  probability,  attempts  to  forecast  as  nearly  as  possible  all 
the  elements  which  may  affect  his  interests.  An  example 
occurs  in  the  Engineering  and  Mining  Journal  for  Decem- 
ber 8,  1904.  It  is  there  stated  that  the  mine  at  Cananea, 
belonging  to  the  Green  Consolidated  Copper  Company,  was 
worth,  according  to  quotations  at  that  time,  $30,000,000. 
This  valuation  the  journal  shows  might  be  justified  if  we 
suppose  the  mine  to  contain  a  total  of  1,040,000,000  pounds 
of  copper  which  can  be  mined  at  the  rate  of  104,000,000 
a  year  for  10  years,  and  if  we  suppose  that  the  price  of  cop- 
per will  be  14  cents,  and  the  cost  of  production  8  cents,  to 
which  should  be  added  the  expense  of  refining,  selling,  com- 
mission, etc.,  making  1\  cents  more,  or  10^  cents  in  all.  If 
we  make  allowance  for  future  economies,  this  may  be  called 
10  cents,  leaving  a  net  profit  of  4  cents  a  pound.  On  this 
basis  we  should  obtain  a  10-year  annuity  of  $4,160,000  per 
annum,  the  present  value  of  which,  at  5  per  cent,  would  be 
$32,000,000.  But  inasmuch  as  these  forecasts  involve 
great  uncertainty,  a  fair  price  would  be  regarded  as  $30,- 
000,000,  the  discrepancy  between  $30,000,000  and  $32,000,- 
000  being  due  to  the  element  of  risk,  i.e.  the  combined  in- 
fluence of  probability  and  caution.  This  price  represents 
a  basis  of  6|  per  cent.2 

1  Nevertheless  it  is  more  than  conceivable  that  the  time  may  come 
when  practical  brokers  will  make  use  of  probability  computations  in 
the  same  way  that  they  now  make  use  of  bond  tables.  The  writer's 
colleague,  Professor  Norton,  has  shown  this  possibility.  For  a  brief 
statement,  see  Appendix  to  Chap.  XVI,  §  3. 

2  For  such  properties  as  mines  which  rapidly  depreciate,  brokers 
often  reckon  the  "basis"  in  a  somewhat  different  manner,  computing 
the  percentage  realized  to  the  investor  on  the  supposition  that  he 
employs  a  depreciation  fund  and  reinvests,  not  at  the  6|  per  cent  just 


284  NATURE   OF   CAPITAL  AND   INCOME     [CHAP.  XVI 

In  forecasting  the  income  from  capital,  it  is  thus  neces- 
sary to  forecast  all  the  elements  which  may  influence 
it  and  also  their  variability.  These  elements  are  some- 
times exceedingly  numerous.  A  stockholder  in  a  railroad, 
in  order  to  obtain  a  true  idea  of  the  value  of  his  property, 
must  look  forward  to  the  traffic  of  the  road,  the  price  which 
can  be  charged  for  this  traffic,  the  cost  of  operation,  in- 
volving the  amount  of  labor,  fuel,  and  materials,  the  prices 
paid  for  these  items,  etc.  To  forecast  any  one  of  these  in- 
volves, in  turn,  some  knowledge  of  outside  conditions,  as 
the  outlook  for  crops,  prices  of  agricultural  products,  prob- 
abilities of  increased  trade  through  connecting  lines,  increased 
density  of  population,  possible  competition,  possible  ad- 
verse legislation,  etc. 

§12 

We  now  see  that  the  value  of  capital  actually  changes 
through  any  one  of  four  causes:  (1)  Through  the  effect 
of  discount ;  that  is,  while  no  income  is  being  received,  the 
value  of  the  capital  will  rise  along  a  discount  curve.  (2) 
Through  the  periodic  detachment  of  income;  that  is,  at 
times  when  income  or  outgo  occurs,  the  capital  will  be 
directly  decreased  by  the  amount  of  the  income  and  in- 
creased by  the  amount  of  the  outgo  reached  and  passed. 
(3)  Through  unexpected  changes  in  the  rate  of  interest; 
that  is,  when  such  changes  occur  causing  revaluations  of  the 
future  by  discounting  it  at  a  new  rate,  the  value  of  the 
capital  will  change  correspondingly  —  increasing  if  the  rate 
of  interest  falls,  and  decreasing  if  it  rises.  (4)  Through 
unforeseen  changes  in  expected  income. 

The  fourth  cause  is  the  one  of  most  practical  importance. 

mentioned,  but  at  the  true  or  safe  rate  of  interest,  5  per  cent.  On 
this  calculation  the  investor  would  be  found  to  make  10  per  cent  per 
annum  in  addition  to  the  amount  set  aside  for  depreciation  at  5  per 
cent,  and  the  "basis"  would  be  called  10  per  cent.  For  the  case  just 
mentioned,  this  10  per  cent  realized,  with  the  depreciation  fund  re- 
invested at  5  per  cent,  is  equivalent  to  6J  per  cent  realized,  with  a 
rein  vestment  at  6J  per  cent. 


SEC.  12] 


THE    RISK    ELEMENT 


285 


The  market  quotations  for  any  product  are  constantly 
being  changed  and  revised,  not  so  much  through  the  opera- 
tion of  the  first  three  principles  as  through  the  fourth — • 
the  constantly  changing  outlook  into  the  future.  Every 
rumor  as  to  crops,  every  storm  or  pest  which  is  known  to 
have  destroyed  them,  changes  the  expectation  of  future  in- 
come. Since  the  third  and  fourth  causes  are  both  due  to 
lack  of  foresight,  they  may  be  included,  if  desired,  under 
the  common  head  of  "risk." 

In  Figure  11  the  operation  of  these  four  causes  is  repre- 
sented as  occurring  successively  in  the  order  enumerated. 
The  capital-value  first  rises  along  the  discount  curve  AB, 


constructed  according  to  a  particular  rate  of  interest. 
When  the  first  income  coupon,  so  to  speak,  BC,  is  detached, 
the  value  falls  to  C,  after  which  it  travels  again  along  the 
discount  curve  CD,  rising  suddenly  when  a  certain 
expected  cost  DE  has  been  gotten  rid  of,  then  following  EF 
again,  whereupon,  in  consequence  of  a  sudden  and  unexpected 
rise  in  tlie  rate  of  interest,  it  falls  to  G,  after  which  it  ascends 
according  to  the  steeper  discount  curve  GH,  and  then,  in 
consequence  of  a  change  in  the  estimate  of  future  income, 
falls  again  to  /,  after  which  it  proceeds  along  another  dis- 
count curve  to  J,  and  so  on  indefinitely.  The  changes 
caused  by  actual  income  and  outgo,  we  here  represent  by 
the  continuous  lines  BC,  DE,  etc.,  and  the  changes  due  to 
a  revised  estimate  of  interest  and  of  income  we  represent  by 
the  dotted  lines  FG,  HI,  etc. 


286  NATURE    OF   CAPITAL   AND    INCOME      [CHAP.  XVI 

§13 

The  discount  curves  just  employed  are  assumed  to  be  the 
same  as  those  employed  formerly  in  the  discussion  of  certain 
prospective  income.  But,  as  a  matter  of  fact,  chance  will 
have  an  effect  even  on  discount  curves.  For  the  increase  of 
capital- value  along  a  discount  curve  is  due  to  the  approach 
of  expected  income,  and  this  approach,  in  the  case  of  uncer- 
tain income,  is  quite  different  from  what  it  is  in  the  case  of 
certain  income.  It  is  only  as  the  owner  has  a  conviction 
that  he  is  nearing  the  time  when  income  will  be  received, 
that  the  capital- value  will  increase  at  all.  This  will  be  true 
of  dividends  for  the  declaration  of  which  there  are  defi- 
nitely appointed  times;  but  if  the  times  for  the  install- 
ments of  income  are  wholly  fortuitous,  the  capital-value 
will  not  increase  and  instead  of  a  discount  curve,  we 
shall  have  a  horizontal  line.  If  a  piano  dealer  is  asked 
to  value  a  particular  piano  in  his  stock,  he  will  not  add 
interest  because  it  had  been  in  his  stock  a  long  time. 
It  is  impossible  for  him  to  say  which  individual  piano  will 
be  sold  next,  and  the  mere  fact  that  a  particular  piano  has 
stood  for  a  long  time  in  his  store  will  offer  no  assurance  that 
it  will  be  sold  earlier  than  the  others.  Therefore  the  value  of 
the  piano  will  not  advance  with  time,  but  will  remain  nearly 
at  the  wholesale  price.  In  the  same  way,  a  stock  of  money 
which  a  man  carries  as  cash  does  not  advance  in  value  by 
lying  in  his  pocket.  For  although  the  services  which  it  will 
render  to  its  owner  are  actually  approaching,  their  exact 
time  of  occurrence  is  not  known,  but  is  subject  to  chance. 
It  is  chiefly  in  the  case  of  bonds  and  stocks,  where  there 
are  definite  times  for  the  occurrence  of  income,  that  the 
actual  value  ascends  strictly  along  the  discount  curve. 
In  the  case  of  shares  of  stock  if  the  stockholder  fears  that 
a  dividend  will  be  small,  the  value  of  the  stock  will  only 
slowly  increase  as  the  time  for  the  dividend  approaches. 
It  will  follow  a  discount  curve,  but  one  which  climbs  toward 


SEC. 13] 


THF-:    RISK    KLKMKNT 


287 


only  a  slight  elevation  —  enough  to  represent  the  commercial 
value  of  the  uncertain  dividend.  Then  when  the  amount 
of  the  dividend  is  known,  just  before  it  is  distributed,  the 
stock  (including  the  right  to  the  impending  dividend) 
will  suddenly  jump  in  value.  After  the  dividend  is  paid, 
it  will  again  descend  and  then  increase  slowly  in  value  until 
the  approach  of  the  next  dividend.  This  will  explain  the 
fact  which  has  sometimes  been  observed,  that  the  value 
of  a  dividend-paying  stock  often  remains  fairly  constant. 
Normally  its  course  will  be  somewhat  as  in  Figure  12. 
The  capital-value  increases  only  slowly  from  A  to  B,  when, 
with  the  declaration  of  a  dividend,  it  immediately  jumps 
to  C,  and  with  the  distribution  of  the  dividend  at  D 


FIG.  12. 

descends  to  E,  and  so  on  indefinitely.  If  we  omit  the 
fluctuations  between  the  declarations  of  dividends  and  the 
distributions,  the  course  of  the  stock  remains  relatively 
horizontal,  as  represented  by  AB,  EF,  IJ. 

§14 

The  introduction  of  the  element  of  chance  does  not  greatly 
affect  bookkeeping  except  to  impair  somewhat  the  corre- 
spondence between  capital  accounts  and  income  accounts. 
This  is  occasioned  by  mere  changes  in  the  size  of  the 
capital  items.  When  revision  of  capital-value  is  clue  to  a 
new  estimate  of  future  income,  as  after  a  fire,  shipwreck, 
or  other  calamity,  the  immediate  result  is  merely  to  reduce 
(or,  it  may  be,  to  increase)  the  value  of  the  assets.  The 
accountant  must  "write  down"  (or  up)  the  assets,  and 


288  NATURE    OF   CAPITAL   AND   INCOME       [CHAP.  XVI 

therefore  also  reduce  the  balancing  item  on  the  other  side, 
called  undivided  profits,  or  profit  and  loss.  But  the  income 
account  is  not  affected  except  as  the  new  outlook  toward 
the  future  may  lead  to  new  expenses  for  reconstruction, 
or  to  new  income. 

§15 

Business  men  try  not  only  to  estimate  the  risks  which 
they  must  encounter  and  to  adjust  their  accounts  accord- 
ingly, but  they  also  endeavor  to  avoid  such  risks  altogether. 
This  follows  from  the  existence  of  the  factor  of  caution. 
Where  the  coefficient  of  caution  is  abnormal,  amounting  to 
mcaution,  risks  are  not  avoided,  but  are  expressly  sought, 
and  the  phenomena  of  gambling  and  indiscriminate  specu- 
lation are  the  result.  But  in  the  great  majority  of  men  there 
exists  a  healthy  fear  of  risks,  and  in  consequence  a  tendency 
to  avoid  or  reduce  them. 

There  are  five  principal  ways  in  which  risks  may  be  re- 
duced, viz. : - 

1.  By  increasing  guaranties  for  the  performance  of  con- 
tracts ; 

2.  By  increasing  safeguards  against  incurring  losses ; 

3.  By  increasing  foresight  and  thereby  diminishing  the 
risks ; 

4.  By  insurance,  that  is,  by  consolidating  risks; 

5.  By  throwing  risks  into  the  hands  of  a  special  class 
of  speculators. 

These  will  be  considered  in  order. 

§16 

The  ownership  of  capital  wealth  necessarily  involves 
risk,  since  the  income  from  it  can  only  be  estimated,  —  never 
precisely  foreknown.  But  it  is  possible,  by  a  division  of 
the  ownership  of  capital  wealth,  for  one  class  of  property 
holders  to  assume  the  burden  of  risks  and  to  guarantee  to 
another  class  a  fixed  income.  This  is  the  primary  reason 


SEC.  16]  THE    RISK    ELEMENT  289 

for  the  separation  of  securities  into  two  great  classes  called 
stocks  arid  bonds.  In  any  large  enterprise  the  stockholders 
take  the  risks,  and  by  so  doing  guarantee  to  the  bond- 
holders a  fixed  income.  As  was  remarked  in  a  previous 
chapter,  the  capital  stock  acts  as  a  buffer  between  the  liabili- 
ties and  the  assets,  which  amounts  to  saying  that  it  guaran- 
tees a  fixed  income  to  the  holders  of  the  liabilities.  Presi- 
dent Hadley  has  emphasized  the  fact  that  a  bondholder 
"commutes"  the  precarious  income  of  an  enterprise  into 
a  fixed  annuity  and  that  the  system  by  which  one  class  re- 
ceives "  interest"  and  another  "  profits"  has  its  origin  in  the 
desire  of  one  class  to  avoid  and  the  willingness  of  another 
to  assume  risks.1 

Nevertheless  the  general  relation  between  creditor  and 
debtor  necessarily  carries  with  it  a  certain  amount  of  risk  to 
the  creditor.  This  risk  may  be  reduced  by  the  deposit  of 
collateral  security  or  endorsement 2  as  in  the  case  of  bank 
loans  and  discounts;  by  mortgage  on  real  estate,  or  occa- 
sionally on  chattels;  by  legal  regulations,  as  in  the  case 
of  notes  of  national  banks,  and  by  other  methods. 

§17 

The  method  of  guaranties  is  really  a  method  of  shifting 
risks  rather  than  of  avoiding  them.  The  second  method 
aims  to  reduce  risk  by  special  safeguards.  Some  articles 

1  But  the  "rate  of  commutation"  is  not  a  rate  of  interest,  since 
any  ratio  of  commutation  is  necessarily  a  ratio  between  two  incomes, 
those  respectively  of  the  stockholders  and  the  bondholders,  whereas 
the  rate  of  interest  is  a  ratio  of  income  to  capital. 

2  The  influence  of    endorsement  in  reducing  risk  is  greater  than 
would  appear  on  the  surface.     Thus,  if  there  is  one  chance  in  a  hun- 
dred that  the  signer  of  a  note  will  default,  and  a  like  chance  for  his 
endorser,  both  these  risks  being  independent,  the  chance  that  the  bank 
will  lose  is  the  product  of  these  two,  or  only  one  chance  in  ten  thou- 
sand.    Hence,  two-name  commercial  paper  is  ordinarily  a  safe  se- 
curity, provided,  of  course,  the  names  are  those  of  reliable  business 
men,  such  as  have  a  high  "  rating  "  in  Bradstreet's  or  other  standard 
commercial  agency. 

u 


290  NATURE    OF   CAPITAL   AND    INCOME        [CiiAP.  XVI 

of  wealth  exist,  in  fact,  simply  for  the  sake  of  meet- 
ing sudden  unforeseen  emergencies.  This  is  true,  for 
instance,  of  fire  engines,  fire  extinguishers,  safety  appliances 
on  railways,  safety  valves,  and  other  devices  connected 
with  steam  engines  and  machinery,  burglar  alarms,  safety 
deposit  vaults,  etc.  To  a  large  extent  this  risk-meeting 
function  applies  to  almost  every  stock  of  wealth.  Food 
in  a  pantry  usually  exists  beyond  certain  wants  in 
order  to  provide  for  uncertain  wants,  and  when  sources 
of  supply  are  distant,  such  stores  of  food  need  to  be  large. 
Especially  is  this  true  in  the  case  of  armies.  Again,  a 
factory  will  usually  have  a  large  reserve  stock,  both  of 
raw  materials  and  finished  products,  in  order  to  meet  un- 
expected demands.  In  like  manner,  jobbers,  wholesalers, 
and  retailers  maintain  a  sufficient  stock  of  goods  to  meet 
not  only  the  foreseen,  but  some  of  the  unforeseen  demands 
of  their  customers.  The  function  of  speculators  in  grain  or 
other  commodities  consists  largely  in  conserving  the  stock 
of  a  community  as  a  safeguard  against  future  scarcity. 
Almost  all  of  what  is  called  the  reserve  of  a  bank  is  used  as  a 
safety  fund  to  meet  the  unforeseen  demands  of  note-holders 
and  depositors,  and,  in  particular,  to  meet  a  special  "run." 
These  reserves  often  remain  as  idle  as  a  fire  extinguisher  for 
years  or  even  decades  against  the  hour  of  need.  It  is  said 
that  there  are  bars  of  precious  metals  in  the  Bank  of  England 
which  have  lain  there  undisturbed  for  two  centuries.  A 
large  part  of  the  cash  carried  by  an  ordinary  individual  is 
quite  analogous  to  a  bank  reserve,  being  held  to  meet  special 
emergencies.  Some  individuals  even  keep  in  a  separate 
pocket  a  special  gold  piece,  lest  some  day  they  should  become 
"stranded."  It  may  be  said  that  this  risk-meeting  function 
of  pocket  cash  is  the  chief  compensation  for  the  so-called 
"loss  of  interest"  on  the  money  thus  carried.  The  con- 
venience and  security  obtained  by  having  an  adequate 
supply  is  a  species  of  income  replacing  the  income  which 
might  be  earned  were  the  sum  invested.  The  same  prin- 


SEC.  18]  THE    RISK    ELEMENT  291 

ciples,  from  the  standpoint  of  an  individual,  apply  to  hank 
deposits,  and  thus  to  the  whole  volume  of  the  circulating 
medium. 

§18 

The  third  method  of  reducing  risks  is  by  increasing 
knowledge.  It  has  been  seen  that  risk  is  nothing  but  an 
expression  of  ignorance,  arid  decreases  with  the  progress 
of  science.  It  may  be  said  that  the  chief  progress  now 
being  made  industrially  consists  in  lifting  the  veil  which 
hides  the  future.  The  countless  trade  journals  now  in 
use  have  their  special  reason  for  existence  in  enabling 
their  readers  better  to  forecast  the  future,  by  supplying 
them  with  data  as  to  past  and  present  conditions,  as  well 
as  by  instructing  them  in  the  relations  of  cause  and  effect. 
The  government  reports  of  crops,  the  technical  schools 
and  agricultural  colleges,  all  tend  in  the  same  direction. 
Whereas  formerly  the  mine  prospector  could  only  guess 
wildly  at  the  ore  "in  sight"  and  the  time  and  cost 
required  to  mine  it,  the  graduate  of  mining  schools  is 
now  able,  through  knowledge  of  geology  and  metallurgy,  to 
bring  these  forecasts  into  some  degree  of  scientific  accuracy. 
And,  whereas  until  recently  farming  was  one  of  the  most 
uncertain  of  occupations,  it  is  to-day  —  thanks  to  modern 
scientific  agriculture  —  almost  if  not  quite  as  amenable 
to  prediction  as  industry  or  commerce. 

§19 

We  come  now  to  that  important  means  of  avoiding 
and  shifting  risks,  called  insurance.  Insurance  involves 
the  offsetting  of  one  risk  by  another:  that  is,  the  consoli- 
dation of  a  large  number  of  chances  whereby  relative  cer- 
tainty is,  as  it  were,  manufactured  out  of  uncertainty. 
To  illustrate  this,  let  us  suppose  that  10,000  houses  of 
the  same  kind  are  too  distant  from  each  other  to  be  de- 
stroyed by  the  same  fire,  and  let  us  suppose  that  these 


292  NATURE    OF    CAPITAL   AND    INCOME        [CHAP.  XVI 

houses  in  the  average  would  be  worth  $10,000  each  were  it 
not  for  the  risk  of  fire;  in  other  words,  that  $10,000  is  the 
capitalized  value  of  the  services  to  be  rendered  by  each 
house,  assuming  that  it  lives  out  its  natural  life.  The 
value  of  the  total  number  of  houses  would  then  be 
$100,000,000.  This  is  the  "  riskless  value."  It  is  the 
capitalized  value  of  the  income  which  the  10,000  houses 
would  bring  in,  were  there  no  loss  by  fire.  If  interest  is 
at  5  per  cent,  the  income  which  is  thus  capitalized  is 
$5,000,000  a  year.  If  now  we  suppose  that  the  annual 
risk  of  fire  is  one  chance  in  200,  there  will  be  about  50 
houses  annually  burned.  Reckoning  the  value  thus  de- 
stroyed at  an  average  of  $10,000  for  each  house,  there 
will  be  $500,000  annually  lost  by  fire.  We  must  now  de- 
duct this  from  the  $5,000,000,  which  would  be  the 
income  were  it  not  for  fires.  We  have  left  $4,500,000, 
the  capitalization  of  wrhich  is  only  $90,000,000.  In 
other  words,  the  total  property  of  10,000  houses  is 
worth  in  "  mathematical  value "  $90,000,000  instead  of 
$100,000,000,  the  reduction  being  because  of  the  prospect 
of  fires.  If  we  suppose  all  of  these  houses  to  be  owned  by 
one  corporation,  this  mathematical  value  of  $90,000,000 
might  also  be  the  actual  value,  for  such  a  corporation 
could  count  on  about  50  houses  burning  annually  almost 
as  a  certainty.  Each  house  would  then  be  worth,  on  an 
average,  $9000.  But  if  such  an  individual  house  is  owned 
by  an  individual  person,  this  mathematical  value  would 
not  be  its  "  commercial  value,"  on  account  of  the  element 
of  caution.  Let  us  say  that  the  caution  coefficient  is  |,  in 
which  case  the  house  would  be  worth  $7000.  In  other 
words,  we  have  $10,000  as  the  "riskless"  value  of  the 
house,  $9000  as  its  "mathematical"  value,  and  $7000  as 
its  actual  "commercial"  value,  assuming  that  there  is  not 
as  yet  insurance.  Now  if  the  owner  of  such  a  house  could 
secure  insurance  on  a  purely  mathematical  basis  of  the 
risk,  which,  as  we  have  seen,  is  one  half  of  one  per  cent, 


SEC.  19]  THE  RISK   ELEMENT  293 

and,  therefore,  could  pay  only  $50  per  annum,  in  consid- 
eration of  which  the  value  of  his  house,  if  destroyed  by 
fire,  is  restored  to  him,  it  is  evident  that  he  has  made  a 
good  investment ;  for  he  is  now  assured  of  a  house  even 
should  a  fire  occur,  and  he  has,  instead  of  the  risk  of  fire, 
merely  to  pay  his  annual  premium  of  $50  a  year,  the  capi- 
talized value  of  which  is  $1000.  Consequently,  liis  house 
is  worth  $10,000-  $1,000,  or  $9000.1 

Such  an  insurance  rate,  however,  being  based  on  the 
mathematical  or  "pure"  premiums,  would  not  pay  any 
profit  to  the  companies  conducting  it.  Rut  even  a  higher 
insurance  would  leave  a  large  margin  of  capital-value  saved 
to  the  insured.  If  we  suppose  a  "loading,"  so  that  the  in- 
surance premium  is  not  $50  but  $100,  similar  reasoning 
would  show  that  the  value  of  the  house  when  insured  would 
be  to  the  owner  $8000  instead  of  $7000.  As  long  as  the 
loading  is  not  sufficient  to  absorb  all  the  margin  between 
the  $7000  and  $9000,  it  will  be  advantageous  to  insure. 

Between  the  case  of  a  man  owning  an  individual  house, 
when  the  element  of  caution  would  have  a  large  influence, 
and  that  where  10,000  houses  are  owned  by  the  same  corpo- 
ration, in  which  case  the  caution  element  is  almost  entirely 
absent,  there  are  numberless  intervening  cases.  The  larger 
the  number  of  houses  owned  by  one  individual  or  corporation, 
the  less  profitable  becomes  insurance.  To  express  it  in  the 
language  of  the  business  man,  the  various  risks  insure  each 
other.  Thus,  the  North  German  Lloyd  Company  finds  it 
profitable  not  to  insure  its  vessels  against  shipwreck,  be- 
cause they  have  so  large  a  fleet  that  their  losses  through 
a  period  of  time  can  be  counted  on  fairly  well  in  advance. 

One  effect  of  insurance  on  the  individual  is  to  steady 
the  income  from  his  property.  The  owner  of  the  house  in 
question  would  receive,  if  it  were  not  insured,  a  net  annual 
income,  after  providing  for  depreciation,  of  5  per  cent  on 
•$10,000,  or  $500  a  year  until  the  house  was  burned,  after 

1  For  a  mathematical  statement,  see  Appendix  to  Chap.  XVI,  §  3. 


294  NATURE    OF    CAPITAL   AND    INCOME       [Cnxp.  XVI 

which  he  would  receive  nothing;  whereas,  if  he  insures,  he 
receives  this  $500  income  less  his  premium  up  to  the  date 
of  the  fire,  and  afterward  the  income  from  the  indemnity 
paid  him  by  the  company. 

§20 

The  same  principles  apply  to  other  forms  of  insurance, 
as  marine  insurance,  which,  by  consolidating  in  an  in- 
surance company  the  risk  on  a  large  number  of  vessels, 
reduces  for  the  individual  even  the  perils  of  the  sea  to 
relative  certainty  and  regularity;  or  as  steam  boiler  in- 
surance, which  in  a  similar  manner  treats  the  risks  of 
explosion;  or  as  plate-glass  insurance,  burglar  insurance, 
live  stock  insurance,  hail  and  cyclone  insurance,  fidelity 
insurance,  accident  insurance,  employer's  liability  insur- 
ance, and,  above  all,  life  insurance.1  This  form  of  insur- 
ance, like  the  other  forms,  tends  to  steady  the  income  of 
the  beneficiary.  If  a  wife  holds  insurance  on  her  hus- 
band's life,  the  consequence  is  that,  although  what  he 
gives  her  during  his  life  is  somewhat  diminished,  her  in- 
come will  not  suddenly  cease  at  his  death.  The  ten- 
dency of  insurance  here  as  elsewhere  is  to  make  regularity 
out  of  irregularity,  relative  certainty  out  of  relative  un- 
certainty; and  where,  under  the  form  of  insurance  con- 
tracts, the  opposite  result  follows,  the  case  is  not  one  of 
true  insurance,  but  tends  to  become  one  of  gambling. 
Thus,  if  a  person  insures  the  life  of  some  one  in  whom  he 
has  no  financial  interest,  he  is  merely  gambling  on  that  per- 
son's life.  Some  years  ago  in  Michigan  there  was  an  abuse 
of  this  type  called  "graveyard  insurance."  Speculators 
went  through  the  form  of  insuring  the  lives  of  certain 
old  persons,  in  other  words  of  betting  on  their  deaths, 
a  procedure  not  only  vicious  as  gambling,  but  calculated 
also  to  lead  to  crime.  The  same  considerations  apply  to 
fire  insurance,  where  a  person  insures  a  building  in  which 
1  See  Appendix  to  Chap.  XVI,  §  4. 


SEC.  21J  THK    RISK    ELEMENT  295 

lie  is  not  financially  interested,  or  over-insures  one  in  which 
he  is.1 

The  range  to  which  insurance  can  apply  is  always  lim- 
ited; hut  it  is  constantly  being  extended,  as  business  men 
learn  how  to  bring  risks  of  any  kind  on  to  a  statistical 
basis  and  to  apply  the  theory  of  probability.  At  present 
the  total  assets  of  life  insurance  companies  alone  in  the 
United  States  are  nearly  $3,000,000,000. 


Where  risks  cannot  be  reduced  to  a  statistical  basis, 
and  therefore  cannot  be  insured  against,  recourse  is  often 
had  to  the  shifting  of  the  risk  into  the  hands  of  those 
who  are  willing  to  take  it.  Such  persons  are  speculators. 
A  speculator  is  usually  one  in  whom  the  caution  factor  is 
not  so  pronounced  as  in  the  ordinary  individual.  In  ex- 
treme cases  he  tends  to  become  a  simple  gambler.  The 
distinction  between  a  speculator  and  a  gambler,  however, 
is  usually  fairly  well  marked.  A  gambler  seeks  and  makes 
risks  which  it  is  not  necessary  to  assume,  whereas  the  specu- 
lator is  one  who  merely  volunteers  to  assume  those  risks 
of  business  which  must  inevitably  fall  somewhere.  A  specu- 
lator is  also  usually  fitted  for  his  work  by  special  knowledge, 
so  that  the  risk  to  him,  owing  to  superior  foresight,  is  at  the 
outset  less  than  it  would  be  to  others.  The  indiscrimi- 
nate prejudice  against  all  speculation,  which  is  so  often  met 
with,  is  beside  the  point ;  for,  were  there  no  speculators,  the 
same  risks  would  have  to  be  borne  by  those  less  fitted  to 
bear  them.  The  chief  evils  of  speculation  flow  from  the 
participation  of  the  general  public,  who  lack  the  special 
knowledge,  and  enter  the  market  in  a  purely  gambling 
spirit.  In  addition  to  suffering  the  usual  evil  consequences 
of  gambling,  they  produce  evil  consequences  for  the  non- 
participating  public  by  causing  factitious  fluctuations 

1  For  the  moral  effects  of  insurance,  see  Insurance  and  Crime,  by 
A.  C.  Campbell,  Putnam's,  1902. 


296  NATURE    OF   CAPITAL   AND   INCOME       [CHAP.  XVI 

in  the  values  of  the  products  or  property  in  which  they 
speculate. 

The  evils  of  speculation  are  particularly  acute  when, 
as  generally  happens  with  the  investing  public,  the  forecasts 
are  not  made  independently.  Were  it  true  that  each 
individual  speculator  made  up  his  mind  independently 
of  every  other  as  to  the  future  course  of  events,  the  errors 
of  some  would  probably  be  offset  by  those  of  others.  Butr 
as  a  matter  of  fact,  the  mistakes  of  the  common  herd  are 
usually  in  the  same  direction.  Like  sheep,  they  all  follow 
a  single  leader.  How  easily  they  are  led  is  shown  by 
the  effect  on  the  stock  market  in  the  year  1904,  when 
Thomas  Lawson  published  scare-head  advertisements  in 
the  newspapers  advising  the  public  to  sell  certain  securi- 
ties. 

A  chief  cause  of  crises,  panics,  runs  on  banks,  etc.,  is 
that  risks  are  not  independently  reckoned,  but  are  a  mere 
matter  of  imitation.  A  crisis  is  a  time  of  general  and 
forced  liquidation.1  In  other  words,  it  differs  from  any 
other  period  in  two  particulars,  viz.  that  the  liquidations 
are  more  numerous,  and  that  they  are  for  the  most  part 
forced  upon  the  debtors  by  the  creditors  because  of  threat- 
ened or  actual  bankruptcy.  Neither  of  these  conditions 
could  exist  unless  there  had  been  at  a  prior  time  a  general 
miscalculation  of  the  future.  Both  creditors  and  debtors 
must  have  made  a  wrong  forecast  when  their  ill-fated  agree- 
ments were  entered  into.  Hence  a  crisis  is  the  penalty 
which  must  be  paid  when  a  previous  general  error  in  pre- 
diction is  discovered.  Such  a  general  error  may  be  due  to 
the  coincidence  of  a  number  of  independent  mistakes  of 
individuals;  but  it  almost  always  is  due  to  lack  of  inde- 
pendence, —  to  the  principle  of  imitation.  The  error, 
whatever  it  is,  when  committed  by  a  person  of  influence,  is 
like  an  infection;  it  is  caught  by  hundreds  of  others  and 

1  See  Juglar,  DCS  Crises  Commer dales,  Paris,  2d  edition,  1889, 
Chapter  I. 


SEC.  21]  THE    RISK    ELEMENT  297 

transmitted  to  thousands.  A  great  mob  of  easily  led  in- 
vestors, eagerly  searching  for  "straight  tips"  which  may 
bring  instant  wealth,  make  their  mistake  in  common,  and 
when  the  mistake  is  disastrous  they  try,  en  masse,  to  escape. 
A  sudden  rush  of  all  the  passengers  on  a  ferry-boat  to  one 
side  will  produce  a  "  list  "  in  the  boat's  position,  and  some- 
times cause  it  to  capsize,  though  the  independent  move- 
ment of  the  individual  passengers  will  seldom  or  never 
produce  disaster.  So  also  the  sudden  general  realiza- 
tion of  unforeseen  danger  on  the  part  of  the  investing 
public  may  submerge  the  craft  of  credit  and  those  whom 
it  has  hitherto  borne  along  in  safety.  In  short,  a  general 
crisis  bears  the  relation  to  individual  bankruptcies  which 
a  general  conflagration  bears  to  individual  fires.  The  key 
to  the  study  of  either  crises  or  conflagrations  is  the  exist- 
ence, in  place  of  independent  hazards,  of  interdependent 
ones.  So  far  as  conflagrations  are  concerned  the  prin- 
ciple of  interdependence  is  distinctly  recognized  by  stu- 
dents of  fire  insurance,  and  in  consequence,  each  company 
strives  to  keep  its  own  fire  risks  independent  of  each 
other,  by  not  having  too  many  in  the  same  locality ;  but 
so  far  as  crises  are  concerned,  the  principle  has  not  yet  been 
sufficiently  emphasized  by  students  of  economic  history. 

The  same  principle  applies  to  the  phenomenon  of  a  run 
on  a  bank.  The  opinions  of  the  bank's  solvency  are  not 
formed  independently  but  interdependently.  A  year  or 
more  ago  the  newspapers  reported  that,  a  policeman  and 
a  crowd  of  people  being  collected  on  the  steps  of  one  of 
the  Wilkes-Barre  savings  banks  to  escape  the  rain,  two 
Hungarian  depositors  who  \vere  passing  jumped  to  the 
conclusion  that  the  bank  had  been  attacked  by  burglars, 
and  circulated  the  disturbing  news  in  the  Hungarian 
colony,  with  the  result  that  when  the  bank  opened  for  busi- 
ness many  depositors  made  a  run  upon  it. 

We  see,  then,  that  where  speculation  is  imitative,  it  is 
dangerous  alike  to  those  who  engage  in  it  and  to  the  public. 


298  NATURE   OF    CAPITAL   AND    INCOME       [CHAP.  XVI 

Where,  on  the  other  hand,  speculation  is  based  on  independ- 
ent knowledge,  its  utility  is  usually  enormous.  It  oper- 
ates both  to  reduce  risk  by  means  of  utilizing  the  special 
knowledge  of  speculators,  and  also  to  shift  risk  from 
those  who  lack  this  knowledge  to  those  who  possess  it. 
The  consequence  is  that  normally  speculative  property  will 
gravitate  into  the  hands  of  those  most  able  to  forecast  its 
true  income. 

Modern  production  has  been  called  capitalistic-specula- 
tive production,  owing  to  the  fact  that  it  is  managed  by 
"captains  of  industry,"  who  are  specially  fitted  at  once  to 
forecast  and  to  mould  the  future  within  the  special  realms 
in  which  they  operate.  The  industries  of  transportation 
and  manufacturing  particularly  are  under  the  lead  of  an 
educated  and  trained  speculative  class,  whose  function  it  is 
to  assume  for  themselves  the  main  risks,  and  leave  the 
ordinary  investor,  who  is  not  so  equipped,  to  cooperate  as 
a  mere  "lender"  or  silent  partner.  Yet  it  often  happens 
that  they  betray  the  confidence  placed  in  them,  and  con- 
tinue to  throw  the  burden  of  risk  on  those  whom  they 
pretend  to  shield. 

§22 

In  the  special  field  more  usually  known  as  "speculative," 
—  namely,  that  in  which  attempts  are  made  to  forecast 
prices  in  the  great  exchange  markets, — we  find  a  similar 
class  who  are  specially  trained.  These  speculators  are 
either  "bulls"  or  "bears";  that  is,  they  speculate  either 
for  a  rise  or  a  fall.  Those  who  believe  that  wheat 
or  any  other  article  is  likely  to  rise  in  value  and  hence 
yield  more  than  the  "rate  of  interest,"  will  hold  it,  or  if 
they  do  not  own  it,  will  buy  it  or  obtain  an  option  on  it. 
Such  an  option  is  known  as  a  "call,"  and  is  put  in  force  at 
a  later  time,  at  a  price  fixed  in  advance  and  considered 
low.  On  the  other  hand,  those  who  believe  that  prices 
will  fall  will  sell  out  their  present  holdings,  or  may  sell 
"short,"  agreeing  to  supply  such  holdings  at  a  later  time 


SEC.  22]  THE    RISK    ELEMENT  299 

at  a  fixed  price  which  they  consider  high.  Such  a  contract 
to  sell  is  often  made  in  the  form  of  an  option,  in  which 
case  it  is  known  as  a  "put." 

To  show  how  such  contracts  will  shift  risks,  a  few  exam- 
ples will  suffice.  A  building  contractor  who  had  taken  a 
large  contract  was  asked  if  he  were  not  taking  large  risks, 
since  he  could  not  foreknow  the  cost  of  building.  He  re- 
plied, "No,  I  am  taking  no  risks  at  all  except  on  'labor'; 
I  have  made  contracts  to  be  supplied  with  all  materials 
when  needed,  at  fixed  prices."  Those  who  made  these  con- 
tracts thus  assumed  the  risk  of  fluctuation  in  price  in  the 
special  materials  in  which  they  dealt,  relieving  the  con- 
tractor of  the  necessity  of  informing  himself  of  the  special 
market  conditions  for  stone,  brick,  timber,  etc.,  and  ena- 
bling him  to  make  a  closer  bid  for  the  contract,  inasmuch 
as  there  was  less  need  of  the  element  of  caution.  The  pub- 
lic, of  course,  get  the  benefit  of  such  a  shifting  of  risk 
in  the  form  of  reduced  cost  of  building.  Similar  results 
follow  from  most  other  "short"  sales.  Again,  a  woolen 
manufacturer  need  not  carry  so  large  a  stock  of  wool  if  he 
can  make  a  contract  by  which  some  one  will  sell  short,  or 
agree  to  supply  the  wool  at  fixed  prices  and  at  certain 
dates.  He  can  afford  to  use  up  his  present  stock  fear- 
lessly, with  the  certainty  that  when  it  is  gone  he  can 
obtain  a  new  supply.1  Without  such  a  contract,  he  would 
be  under  the  necessity  of  carrying  a  large  and  idle  stock. 

An  important  method  of  shifting  risks  is  "hedging," 
whereby  a  dealer,  for  instance  in  transporting  wheat,  may 
be  relieved  of  the  risk  of  a  change  in  price.  He  buys 
wheat  in  the  West  intending  to  ship  it  to  New  York  and 
sell  it  there  at  enough  to  cover  cost  of  transportation 
and  a  small  profit.  In  consequence  of  a  sudden  fall  in 
price  he  might  find  all  his  profit  wiped  out;  or  he  might, 
on  the  other  hand,  by  a  rise  in  price,  make  much  more 
than  normal  profits.  But,  being  of  a  cautious  disposition, 

1  Cf.  Hadley,  Economics,  Putnam's,  1S96,  p.  106. 


300  NATURE    OF   CAPITAL   AND    INCOME       [CHAP.  XVI 

he  prefers  an  intermediate  course,  —  a  small  profit  which 
is  sure,  rather  than  the  chances  of  both  gain  and  loss. 
Consequently  he  "hedges."  He  enters  into  some  specu- 
lative market,  knowing  that  it  will  move  in  sympathy 
with  the  New  York  market,  and  there  he  "speculates" 
for  a  fall,  or  sells  "short."  In  case  the  price  in  New  York 
falls,  what  he  loses  on  the  wheat  which  he  has  transported 
he  gains  through  his  speculative  short  selling.  Contrari- 
wise, if  the  price  rises,  what  he  gains  on  his  wheat  trans- 
ported he  loses  in  the  speculative  market.  In  other  words, 
he  is,  as  it  were,  betting  on  both  sides  of  the  market  at 
once,  and  therefore  eliminating  all  risk,  so  that  he  only 
obtains  his  normal  profit,  commission,  or  percentage  on 
the  actual  wheat  handled,  having  imposed  the  burden  of 
risk  of  speculation  on  the  speculative  dealers  to  whom  he 
sold  short.1 

The  effect  of  hedging  on  those  who  engage  in  it, 
such  as  the  wheat  dealers,  is  evidently  to  enable  them  to 
work  on  a  smaller  margin  of  profit.  In  consequence  the 
public  receives  a  benefit  in  lowered  prices.  The  case  is 
thus  very  similar  to  those  respectively  of  the  builder  and 
of  the  woolen  manufacturer.  Short  selling,  binding  the 
future  to  the  past,  enables  the  specialist  to  guarantee 
to  the  general  public  a  definite  foreseen  series  of  events. 
The  beneficial  effect  to  the  public,  in  saving  useless  stocks 
and  reserves,  in  producing  more  intelligent  direction  of  en- 
terprises, and  in  encouraging  accumulation  through  greater 
certainty  of  its  future  benefits,  is  both  obvious  and  great. 
Risk  is  one  of  the  direst  economic  evils,  and  all  of  the  de- 
vices which  aid  in  overcoming  it  —  whether  increased  guar- 
anties, safeguards,  foresight,  insurance,  or  legitimate  specu- 
lation —  represent  a  great  boon  to  humanity. 

1  See  "Speculations  on  Stock  and  Produce  Exchanges  of  the  United 
States,"  by  Henry  C.  Emery,  Publications  of  American  Economic  Asso- 
ciation. For  the  development  of  insurance-speculation  in  England, 
see  "  The  Put  and  Call,"  by  L.  R.  Biggins,  London,  Effingham  Wil- 
son, 1002. 


PART   IV.     SUMMARIES 

CHAPTER     XVII.     SUMMARY  OF  PART  III 
CHAPTER  XVIII.     GENERAL  SUMMARY 
GLOSSARY.  SUMMARY  OF  DEFINITIONS 


CHAPTER  XVII 

SUMMARY    OF    PART    III    (CHAPTERS    XI-XVl)    REPRESENTED 
BY   DIAGRAMS 


WE  have  finished  our  study  of  the  relations  between 
capital-value  and  income-value  and  may  now  pause  to 
summarize  them  briefly.  At  the  beginning  of  Part  III  it 
was  stated  that  the  income  from  capital  wealth  consists 
of  whatever  service  it  performs  for  man ;  that  capital  and 
income  may  each  be  measured  either  in  specific  quantities 
of  their  respective  units,  or  in  value ;  and  that  consequently 
there  are  four  ratios  between  income  and  capital;  namely, 
(1)  the  physical  productivity  of  capital,  (2)  the  value  pro- 
ductivity, (3)  the  physical  return,  and  (4)  the  value- 
return.  Our  special  theme  has  been  the  value-return,— 
the  relation  between  income-value  and  capital-value. 

We  saw  that  the  value  of  capital  wealth  is  the  discounted 
value  of  its  expected  income.  The  relation  between  the 
value  of  the  income  and  the  value  of  the  capital  was  indi- 
cated by  diagrams.  Income  was  represented  by  a  series 
of  vertical  lines  as  in  Figure  13  (a,  a',  a",  a'"),  the  hori- 
zontal distances  between  them  representing  intervals  of 
time.  It  was  then  found  possible  to  represent  the  capital- 
value  of  this  income  in  anticipation,  on  the  assumption 
that  the  income  could  be  relied  upon  with  certainty. 
This  representation  gave  the  capital  curve,  —  a  broken  or 
toothed  curve  AB.  In  this  curve,  each  vertical  drop  is 
equal  to  the  corresponding  income  item  shown  below  it, 
and  the  intervening  points  are  connected  by  discount 

303 


304 


NATURE   OF   CAPITAL   AND   INCOME       [CHAP.  XVII 


curves;  so  that  the  total  capital- value  at  the  time  C  is 
represented  by  the  altitude  BO. 

But  this  separate  representation  for  capital  and  for  in- 
come respectively  need  not  be  adhered  to,  because  the 
capital  curve  AB  alone  contains  in  its  vertical  teeth  all 
that  is  necessary  to  indicate  the  installments  of  income ;  and 
in  the  present  chapter  the  main  propositions  relating  to 


FIG.  13. 


capital  and  income  will  be  restated  with  the  aid  of  geo- 
metrical representations  of  which  this  capital  curve  AB 
is  the  type. 


First  of  all,  such  a  curve  exhibits  the  fact  that  the  value 
of  any  capital  is  the  discounted  value  of  the  expected  in- 
come. In  Figure  14  the  several  discount  curves  used  in 
previous  diagrams  are  all  continued  to  meet  CB.  The 
parts  into  which  CB  is  thus  divided,  b,  b',  b"  ,  b'",  will 
represent  respectively  the  present  values  of  the  income 
items  a,  a',  a",  a"'.  This  may  readily  be  proved  from 
the  nature  of  the  discount  curves. 


SEC.  2] 


SUMMARY    OF    PART   III 


305 


The  diagram  shows,  in  the  second  place  (tracing  it  for- 
ward chronologically),  that  the  capital-value  alternately 
rises  and  falls,  rising  in  anticipation  of  approaching  income 
and  falling  as  the  installments  of  this  income  are,  like  cou- 
pons, successively  detached  from  capital.  The  alternate  rise 
and  fall  of  the  capital  curve  may  be  equal,  each  to  the  other, 
indicating  that  the  income  is  "standard";  or  the  former 


FIG.  14. 

or  the  latter  may  be  the  greater,  indicating  respectively 
that  the  income  is  above  or  below  standard. 

If  any  installment  of  income  is  negative  —  in  other 
words,  is  not  strictly  income,  but  outgo  —  we  need  simply 
to  reverse  the  direction  of  one  of  the  teeth,  as  in  Figure 
15.  In  this  case  the  capital- value  is  simply  the  discounted 
value  of  the  future  income  less  that  of  the  outgo. 

§3 

As  we  have  seen,  if  we  trace  the  entire  history  of  a  capital 
curve  backward  in  time  from  the  last  installment  of  income 
to  the  beginning  of  the  investment  or  enterprise,  the  curve 


306 


NATURE   OF   CAPITAL  AND   INCOME        [CHAP.  XVII 


will  normally  be  at  the  zero  point  at  both  ends.  This 
is  shown  in  Figure  16.  Such  a  curve  shows  the  normal 
cycle  of  capital-value  from  the  moment  when  the  article 
of  capital  is  first  utilized  to  the  moment  when  it  is  ex- 


FIG.  15. 

hausted.  It  is  "normal"  in  the  sense  that  the  income  is 
just  sufficient  to  compensate  for  the  outlay,  no  more  and 
no  less,  and  that  usually  the  principal  items  of  outgo  all 
occur  in  the  early  part  of  the  cycle,  and  the  principal 
items  of  income  all  accrue  in  the  latter  part.  In  such  a 


normal  curve  the  capital-value  (AB  in  Fig.  16)  at  any 
moment  may  be  said  to  represent  two  things :  first,  it  rep- 
resents the  discounted  value  of  the  future  expected  income 
(less  that  of  future  expected  outgo,  if  any) ;  and,  secondly, 


SEC.  3] 


SUMMARY   OF    PART   III 


307 


it  represents  the  accumulated  value  of  past  outgo  (less  that 
of  past  income,  if  any).  From  this  it  follows  that  the 
value  of  the  capital  AB  is,  on  the  one  hand,  less  than 
the  future  total  income  which  it  represents,  and  greater 
than  the  past  outgo.  This  capital-value  may  be  regarded 
as  made  up  of  the  elements  b,  b',  b'" ,  which  are  respec- 
tively the  discounted  values  of  the  respective  larger  mag- 
nitudes a,  a',  a" ';  and,  on  the  other  hand,  as  made  up  of 


A 
FIG.  17. 

b'",  6iv,  bv,  which  are  the  accumulated  values  of  the  respec- 
tive smaller  magnitudes  a'",  aiv,  av.  By  putting  together 
the  elements  of  wrhich  AB  is  composed,  we  see,  on  the  one 
hand,  that  AB  is  less  than  the  anticipated  income  and 
greater  than  the  past  outgo;  and  consequently,  a  fortiori, 
that  the  past  outgo  is  less  than  the  future  income.  For 
the  sake  of  simplicity  in  our  illustration,  we  have  chosen  a 
point  of  time  after  all  the  outgo  and  before  any  of  the  in- 
come has  accrued ;  but  the  same  principles  could  be  worked 
out  upon  such  a  diagram,  no  matter  what  point  of  time  were 
chosen.  In  other  words,  in  the  normal  case  the  value  of  any 
capital  is  intermediate  between  the  value  of  its  past  cost 
of  production  or  acquisition  and  the  value  of  its  future 
income. 


308 


NATURE   OF   CAPITAL  AND   INCOME         [CHAP.  XVII 


In  the  special  case  in  which  there  is  but  one  item  of  cost 
and  one  item  of  income,  the  curve  is  reduced  to  that  shown 
in  Figure  17,  where  a  is  the  expected  income,  and  o!  the 


FIG.  18. 


past  outgo.     If  the  capital-value  AB  be  taken  at  a  point 
midway  between  the  income  and  outgo,  it  evidently  fol- 


6" 


c" 


FIG.  19. 


lows,  by  the  nature  of  the  discount  curve,  that  the  ratio 
of  a'  to  AB  is  the  same  as  the  ratio  of  AB  to  a,  or  that 


Fii;.  L'O. 


AB  is  the  "mean  proportional,"  or  "geometric  mean," 
between  a  and  a'.  In  other  words,  the  normal  relation 
between  cost,  capital,  and  return  is  expressed  in  the  state- 


SBC.  4]  SUMMARY    OF    PART    III  309 

inent  that  the  capital  is  a  mean  proportional  between  its 
past  cost  and  its  future  return. 

§4 

Another  use  which  may  be  made  of  the  diagrammatic 
representation  is  to  exhibit  in  a  compact  manner  the  sum- 
mation of  both  the  capital  and  the  income  of  any  given 
enterprise  or  community.  This  may  be  done  simply  by 


-N 

— G 


adding  together  the  corresponding  ordinates  or  vertical 
lines  in  any  number  of  capital  curves,  representing  any 
number  of  articles  of  wealth  or  property.  Let  Figure  18, 
for  instance,  represent  one  capital  curve,  and  Figure  19  an- 
other. Figure  20,  formed  by  combining  Figures  18  and  19, 
then  represents  the  sum  of  the  capital  and  income  of  both. 
Figure  20  is  derived  from  Figures  18  and  19  in  such  a 
manner  that  the  ordinate  B  is  the  sum  of  the  individual 
ordinates  bf  and  b",  and  in  like  manner  any  other  ordinate, 
G,  is  the  sum  of  the  corresponding  individual  ordinates  c' 
and  c" '.  From  the  rule  by  which  Figure  20  is  constructed, 
it  is  evident  that  every  tooth  in  the  constituent  curves, 
such  as  a'  and  a",  will  be  reproduced  in  the  combined  dia- 
gram. In  Figure  20,  therefore,  the  ordinates  represent  the 
combined  capital-values  at  various  points,  while  the  two 
teeth  a"  and  a'  represent  the  total  income  accruing  in  that 
time  interval  which  includes  them.  Thus,  Figure  20  epito- 
mizes the  summation  both  of  capital  and  income. 


310 


NATURE    OF   CAPITAL   AND   INCOME         [CHAP.  XVII 


But  it  is  not  necessary  to  have  three  separate  diagrams. 
It  is  possible  to  superimpose  one  of  the  first  two  figures 
upon  the  other,  as  shown  in  Figure  21.  In  this  figure,  on 
the  same  axis  XY  is  drawn  first  FG,  corresponding  to  Fig- 
ure 18  above,  and,  secondly,  at  distances  above  FG  corre- 
sponding to  the  ordinates  in  Figure  19,  is  drawn  the  line 
MN.  This  line  MN  contains  an  apparent  tooth  or  break 
which  does  not  appear  in  Figure  19,  but  this  is  only  for 
the  purpose  of  preserving  at  this  point  the  prescribed  dis- 
tance from  the  line  FG.  Considered  relatively  to  FG  there 


FIG.  22. 

is  no  break.  Thus  the  line  MN,  measured  relatively  to 
FG,  takes  the  place  of  the  constituent  curve  of  Figure  19, 
and  measured  relatively  to  the  base  line  XY  it  represents 
the  combined  curve  of  Figure  20  for  both  constituents. 

The  same  method  applies  where  there  are  any  number  of 
constituent  capital  curves.  Thus  (Fig.  22),  let  us  draw  for 
our  first  capital  curve  one  which  has  an  income  item  a, 
and  superimpose  upon  it  a  second  capital  curve,  of  which 
the  income  item  is  a',  and  so  on.  The  capital  curve  at 
the  top  will  represent  the  total  of  the  individual  capital 
curves  beneath  it,  and  each  belt  between  —  namely,  the 
difference  between  any  two  neighboring  capital  curves  - 
will  replace  a  constituent  curve.  From  the  manner  of 
their  construction  it  is  clear  that  the  income  item  a'  will 
be  carried  forward  successively  to  each  of  the  curves  above 
it,  and  will  be  represented  by  a  tooth  in  the  curve  at  the 


SKC.  5] 


SUMMARY    OF    PART   III 


311 


top,  as  represented  by  the  dotted  lines.  Similarly,  a' ,a",  and 
a'"  are  transmitted  to  the  top.  The  final  curve  at  the 
top  thus  shows  in  its  separate  teeth  all  the  income  items 
contained  in  the  curves  of  which  it  is  the  sum. 

§5 

In  case  two  teeth  in  separate  curves  occur  at  the  same 
instant,  the  combined  curve  will,  of  course,  have  a  large 


Logging  Camp 


FIG.  23. 

tooth  equal  to  their  sum.  In  case  one  tooth  is  positive, 
representing  income,  and  the  other  is  negative,  or  outgo, 
the  coincidence  of  these  will  result  in  a  small  tooth  equal  to 
their  difference,  and  this  difference  will  be  zero  if  the  two 
items  are  equal. 

The  most  important  case  of  this  kind  occurs  when  there 
are  "interactions."  It  has  been  explained  that  an  interaction 
is  an  income  item  for  one  capital  which  at  the  same  time 
is  an  outgo  item  for  another.  If  tiie  curves  for  these  two 
capitals  are  superimposed,  the  equal  income  and  outgo  items 
will  cancel,  and  the  resulting  combined  curve  will  be  un- 
broken at  the  point  representing  the  time  of  interaction. 
This  is  shown  in  Figure  23,  giving  the  typical  history  of 
lumber  operations.  Every  year  a  logging  camp  yields  a 


312 


NATURE    OF   CAPITAL   AND   INCOME        [CHAP.  XVII 


certain  amount  of  logs,  the  turning  out  of  which  is  credited 
to  the  camp,  but  debited  to  the  mill.  In  the  diagram, 
the  space  between  the  base  line  and  the  first  curve  above 
it  represents  the  capital  curve  of  the  logging  camp,  and 
the  space  above  this  curve  represents  the  capital  curve  of 
the  sawmill.  At  the  time  of  the  transfer  of  logs  from 
the  one  category  to  the  other,  there  is  a  corresponding 
diminution  in  the  capital-value  of  the  logging  camp,  but 
an  increase  in  the  capital- value  of  the  sawmill. 

The  characteristic  of  such  an  interaction  or  couple  is 
that  it  leaves  unbroken  the  upper  curve  of  final  summation. 


Sapling 


Tree 


There  is  no  carrying  forward  of  teeth,  as  by  the  dotted  lines 
in  the  previous  diagram,  —  or  rather,  the  carrying  forward 
results  in  a  cancellation.  The  interaction  is  merely  a 
sacrifice  of  one  capital  for  the  benefit  of  another,  and  does 
not  disturb  the  total. 

If  the  interaction  BC  is  greater  than  we  have  represented 
it  in  the  diagram,  so  that  C  is  lower  and  B  higher  than  in- 
dicated, the  discount  curve  AB  will  be  nearer  coincidence 
with  MN,  and  CD  nearer  coincidence  with  XY.  We  may 
suppose  a  case  in  which  coincidence  is  reached.  This  case 
is  represented  in  Figure  24.  Here  BC  represents  such  an 
interaction  as  occurs  when  one  capital  good  is  completely 
transformed  into  another,  as  when  the  "sapling"  becomes  a 
"  tree  "  at  a  certain  definite  point  of  time.  The  capital- value 


SEC.  5] 


SUMMARY    OF    PART   III 


313 


of  the  sapling  disappears  at  BC,  but  there  appears  in  its 
stead  the  capital-value  of  the  tree.  The  change  from  one 
to  the  other  is  evidently  entirely  nominal,  and  it  is  possi- 
ble, by  drawing  any  other  vertical  line  than  BC,  to  create 
an  "  interaction "  simply  by  calling  the  portion  on  the  two 
sides  of  this  line  by  different  names. 

When,  as  in  Figure  25,  a  series  of  curves  is  constructed 
and  superimposed  to  represent  the  income  from  any  speci- 
fied group  of  capital  instruments,  the  sum  total  of  the  income 
is  evidently  represented  by  the  entire  series  of  teeth  in  the 


FIG.  25. 


top  curve.  These  teeth  form  a  physical  picture  of  the 
"outer  fringe"  of  services,  which  was  discussed  in 
previous  chapters.  If  in  the  diagram  we  omit  the  upper- 
most layer  of  capital,  the  curve  remaining  immediately 
below  this  layer  will  then  be  the  outer  fringe  for  the  entire 
series  of  capital  instruments  below  it.  We  may  pro- 
ceed step  by  step  in  either  direction,  leaving  off  an  item  of 
capital  or  taking  one  on.  In  every  case  the  outer  fringe 
of  teeth  will  represent  the  sum  total  of  income  for  the  group 
of  capital  represented  below  it. 


314 


NATURE    OF    CAPITAL   AND    INCOME        [CHAP.  XVII 


In  Figure  25  all  the  teeth  below  the  top  layer  are  rep- 
resented to  be  interactions.  But  if  any  of  them  should 
be  final  services,  they  need  only  be  carried  forward  by  dotted 
lines  to  the  top,  as  in  Figure  26.  Or  if  the  capital  repre- 
sented by  one  layer  interacts  with  the  capital  represented 
by  a  layer  two  or  more  removes  above  it,  the  connection 


FIG.  26. 

will  be  represented  by  carrying  forward  the  tooth  by  dotted 
lines  to  the  proper  stage. 

As  we  are  at  present  interested  in  the  general  aspects 
of  the  subject,  we  need  not  take  into  account  such  complica- 
tions, but  may  assume,  for  purposes  of  exposition,  that  all 
capital  can  be  arranged  in  a  single  definite  series,  each  mem- 
ber of  which  acts  upon  the  one  above  it,  and  so  on  to  the 
end.  In  the  actual  world,  it  is  usually  possible  to  arrange 
capital  roughly  in  such  an  interacting  series. 


Two  special  applications  may  be  made  of  the  foregoing 
representation  for  the  summation  of  capital  curves.  The 
first  will  show  the  total  value  of  capital  property  and  the 
total  value  of  income  possessed  by  a  particular  individual, 
and  the  second  will  show  the  same  condition  as  to  an  entire 
society. 


SEC.  6] 


SUMMARY    OF    PART    III 


315 


We  may  suppose  a  man's  capital  to  1x3  divided  into 
three  classes:  first,  money-paying  investments;  second, 
money;  third,  enjoyable  articles  purchased  by  money. 
We  may  juxtapose  these  elements,  as  in  Figure  27. 


Enjoyable  Capital 


Money 


Investments 


Here,  whenever  an  investment  pays  money,  a  tooth 
is  produced  in  the  first  curve  and  a  transaction 
takes  place  between  the  categories  ''investments"  and 
"money."  By  each  such  transaction  the  investments  are 
reduced  in  value  by  the  amount  of  coupons  detached,  and 
the  stock  of  money  is  increased  by  the  same  amount.  In 
like  manner,  every  time  money  is  spent,  a  transaction  takes 
place  between  the  belt  representing  money  and  that  repre- 
senting enjoyable  capital.  By  such  transaction  the  money 
stock  is  depleted,  and  the  value  of  the  enjoyable  capital 
increased  by  the  same  amount.  These  operations  are 


316  NATURE    OF   CAPITAL   AND    INCOME       [CHAP.  XVII 

therefore  self-canceling  and  are  not  transmitted  to  the 
outer  fringe.  The  total  income,  therefore,  from  the  entire 
group  of  capital,  is  represented  simply  by  the  vertical  un- 
dulations in  the  top  curve. 

By  means  of  this  diagram  we  may  see  clearly  the  various 
meanings  of  "individual  income."  The  business  man 
usually  applies  the  term  to  the  teeth  of  the  investment 
curve ;  the  economist  to  the  teeth  next  above  in  the  money 
curve,  or  the  teeth  above  that  in  the  curve  representing 
enjoyable  capital.  Practically,  it  does  not  greatly  matter 
which  of  the  three  we  select,  since  usually,  for  any  con- 
siderable period  of  time,  all  will  closely  correspond.  This 
must  needs  be  so,  unless  the  stock  of  money  or  enjoyable 
articles  is  appreciably  increasing  or  decreasing.  These 
exceptional  cases  have  already  been  discussed  in  detail, 
and  there  is  no  difficulty  in  representing  them  by  diagrams. 


The  other  application  of  our  diagrammatic  summation  is 
to  present  a  fairly  complete  picture  of  the  total  value  of 
capital-wealth  and  the  total  value  of  income  of  an  entire 
society.  In  the  capital  of  a  community  it  is  not  usual  to 
include  human  beings,  and  for  that  reason  it  is  scarcely 
worth  our  while  to  discuss  the  theoretical  questions  as  to 
the  manner  in  which  they  might  be  included  in  such  a  rep- 
resentation. As  a  matter  of  fact,  the  method  of  capitaliz- 
ing human  beings  will  vary  with  the  special  purpose  in 
view.  Our  present  purpose  is  chiefly  concerned  with  in- 
teractions between  man  and  other  capital,  and  we  need 
practically  only  to  capitalize  the  money-earning  power  of 
the  individual.  This  part  of  the  capital- value  of  a  man 
we  may  call  "labor  power."  We  then  have  the  total  capi- 
tal of  a  community  consisting  of  labor  power,  land,  inter- 
mediate capital,  and  enjoyable  capital,  as  in  Figure  28. 
For  convenience,  and  to  avoid  needless  complications,  we 
assume  that  labor  power  interacts  only  with  land,  land 


SEC. 7] 


SU.M.MAllY    OF    PART    III 


317 


with  intermediate  capital,  and  intermediate  capital  with 
enjoyable  capital.  The  income  from  the  entire  series  is 
represented,  as  before,  by  the  teeth  of  the  uppermost  line. 
From  this  diagram  we  see  that  the  total  income  of  a  com- 
munity comes  through  enjoyable  goods.  The  other  capital 
items  produce  income,  but  this  income  is  in  every  case  also 


Land 


Labor-power 


an  outgo  with  reference  to  the  layer  of  capital  next  above. 
Many  of  the  fallacious  methods  of  summing  income  consist 
virtually  in  adding  together  the  teeth  in  the  various  layers. 
It  is  forgotten  that  the  teeth  below  the  top  layer  are  interac- 
tions and  therefore  both  positive  and  negative  —  positive 
with  reference  to  the  layer  below  and  negative  with  refer- 
ence to  that  above  —  and  that  therefore  they  come  into 
the  summation  of  income  only  to  go  out  again.  Their 
function  in  each  case  is  simply  to  keep  up  the  capital  in  the 
layers  above.  Without  their  activities  these  layers  above 
would  soon  be  exhausted,  and  the  income  at  the  top  would 
not  continue  for  long. 

§8 

From  this  point  of  view,  each  interaction  may  be  con- 
sidered as  the  discounted  value  of  a  certain  portion  of  the 


318 


NATURE    OF   CAPITAL   AND    INCOME       [CHAP.  XVII 


items  of  income  from  the  layer  next  above.  In  Figure 
29  the  interaction  a  may  be  taken  as  the  discounted  value 
of  the  income  taken  from  the  layer  next  above,  between 
the  points  P  and  Q.  Here  we  have  a  geometrical  repre- 
sentation of  the  fact  so  often  insisted  upon  by  Professor 
Bohm-Bawerk l  and  Professor  Taussig,2  that  the  pro- 
duction of  this  year's  wool  is  for  next  year's  (or  next 
month's)  yarn,  of  this  year's  yarn  for  next  year's  cloth,  of 
this  year's  cloth  for  next  year's  clothes,  etc. 

In  tracing  the  connection  between  the  income  items  in 
different  layers,  we  may  consider  either  a  cross-section  be- 
tween the  different  layers,  by  drawing  two  vertical  lines 


FIG.  29. 

separated  by  a  certain  interval  and  noting  the  intervening 
income  taking  place  simultaneously  in  the  various  layers; 
or  we  may  follow  the  successive  time  connections  involved 
between  one  layer  and  the  next.  In  the  treatment  which 
has  been  given  in  the  previous  chapters,  the  former  method 
was  employed.  The  present  diagrammatic  representation 
gives  us  a  bird's-eye  view  of  both.  Thus,  in  Figure  30, 
representing  the  logging  camp,  sawmill,  lumber  yard,  etc., 
having  selected  a  period  represented  between  the  vertical 
line  drawn  at  A  and  B,  we  may  either  address  ourselves  to 
the  mutual  relations  of  the  various  layers  there  comprised ; 
or  we  may  address  ourselves  to  the  income  item  a,  whose 

1  Positive  Theory  of  Capital,  English  translation.  1S90,  pp.  179-1S9. 

2  Wages  and  Capital,  New  York  (Apple-ton),  1896,  Chapters  II,  III. 


SEC.  8] 


SUMMARY    OF    TART    III 


319 


influence  traverses  the  entire  section.  It  is  produced  by 
the  logging  camp ;  "ripens"  into  all  that  income  of  the  saw- 
mill which  is  comprised  between  the  points  P  and  Q;  and 
this  in  turn  ripens  into  the  income  of  the  lumber  yard 


comprised  between  the  points  P1  and  Q'.  In  this  way  we 
are  virtually  following  the  log  as  it  is  transformed  in  the 
various  processes  from  tree  to  lumber. 

It  is  in  consideration  of  such  a  relation  or  set  of  relations 
that  an  income  item  like  a  was  called  a  "preparatory 
service."  Each  such  preliminary  process  of  production 
takes  place  in  anticipation  of  future  resulting  processes, 
and  derives  its  value  from  them.  Combining  this  principle 
with  the  principle  that  the  value  of  all  capital  is  the  dis- 
counted value  of  its  expected  income,  we  see  that  the  value 
of  the  capital  in  the  lower  layers  is  ultimately  dependent 
on  the  value  of  the  income  in  the  topmost  layer:  for  the 
value  of  that  earlier  capital  is  the  discounted  value  of  the 
income  it  produces,  and  this  income,  consisting  of  interac- 
tions or  preparatory  services,  is  in  turn  the  discounted  value 
of  the  services  to  which  it  leads,  and  so  on  through  succes- 


320 


NATURE    OF   CAPITAL   AND   INCOME       [CHAP.  XVII 


sive  layers  to  the  top,  as  seen  in  Figure  31.  Here  AB, 
the  capital-value  of  the  lowest  layer,  is  the  discounted 
value  of  the  income  from  that  layer,  namely  the  teeth 
a,  a',  a",  but  this  income  in  turn  is  the  discounted  value 
of  the  income  represented  by  the  teeth  intervening  be- 
tween P  and  Q  from  the  layer  next  above,  and  this  income 
in  turn  is  the  discounted  value  of  the  income  between  P' 


Q 


FIG.  31. 


and  Qf  on  the  layer  still  above.  In  this  representation 
the  curves  are  shown  as  all  terminating  in  the  base  line ; 
but  the  representation  may  readily  be  extended  to  the  case 
of  an  income  infinitely  continued. 

§9 

In  Chapter  XVI  it  was  shown  that  certain  modifications 
needed  to  be  introduced  into  our  theory  of  the  determina- 
tion of  capital-value  when  the  element  of  uncertainty  was 
introduced.  We  are  fresh  from  the  discussion  of  these,  and 
they  need  no  extended  mention  here.  The  main  point  to 
be  kept  in  mind  is  that  when  the  element  of  chance  is 
taken  into  account,  sudden  breaks  occur  in  the  capital  curve, 
so  that  instead  of  following  the  simple  order  previously 
indicated,  beginning  at  zero  and  ending  at  zero,  with  inter- 
mediate teeth  alternately  rising  and  falling  along  the  dis- 
count curve,  it  suffers  additional  interruptions  at  points 
where  the  estimates  of  future  chances  are  changed. 

The  most  important  point  in  the  life  history  of  such  a 


SEC.  9]  SUMMARY    OF    PART   III  321 

curve  of  capital-value  is  at  the  beginning.  When  the  ele- 
ment of  chance  or  luck  is  taken  into  account,  the  capital 
curve  is  less  likely  to  begin  at  the  zero  line.  It  may  begin 
at  some  point  above ;  it  will  not  begin  at  any  point  below ; 
for  if  the  present  value  of  the  chance  of  gain  did  not  out- 
weigh the  present  value  of  the  chance  of  loss,  the  enterprise 
would  never  be  undertaken  at  all.  In  the  great  majority 
of  cases,  the  capital- value  at  the  outset  of  an  enterprise 
is  greater  than  zero;  that  is,  in  the  estimation  of  those  who 
enter  into  it,  the  gains  will  not  only  pay  for  the  costs  with 
interest,  but  something  in  addition,  even  when  the  element 
of  chance  is  included  in  the  discounting  operation.  At  any 
rate,  it  is  not  infrequent  that  when  a  new  enterprise 
is  started,  those  who  have  the  first  knowledge  of  the 
possibilities,  and  the  first  opportunity  to  exploit  them, 
expect  returns  out  of  proportion  to  the  ordinary  rate  of 
interest  and  compensation  for  risk.  The  only  reason  this 
is  not  more  generally  true  is  because  of  the  existence  of 
competition,  by  which  the  special  advantage  of  individuals 
through  special  knowledge,  foresight,  etc.,  is  offset  by  the 
vigilance  of  their  rivals. 

With  these  points  in  mind,  we  observe  that  the  history 
of  the  value  of  any  particular  article  of  capital-wealth  may 
be  represented  as  in  Figure  32.  Starting  at  A,  some  point 
above  the  zero  line,  the  capital-value  rises  to  B,  because, 
let  us  say,  of  the  first  expenditure  involved.  From  B  it 
proceeds  along  a  discount  curve  to  C.  There,  through  the 
influence  of  the  risk  element,  it  suddenly  drops  to  D,  at 
which  point  some  new  information  has  reduced  the  prospect 
of  future  gain  or  increased  the  risk  of  future  loss.  From  D  in 
turn  it  proceeds  along  the  discount  curve  to  E.  At  this  point 
the  cost  EF  is  incurred,  but  at  the  same  time  confidence  as 
to  the  future  receives  a  shock,  and  instead  of  proceeding 
from  F,  the  curve  drops  at  once  to  G.  Thence  it  rises  gradu- 
ally and  normally  to  H,  when  the  first  income  item,  HI, 
is  received.  This  being,  let  us  say.  less  than  was  anticipated, 


322 


NATURE    OF   CAPITAL   AND    INCOME        [CHAP.  XVII 


it  shows  that  the  capital-values  had  been  hitherto  too  high. 
Consequently  the  curve  drops  to  J,  and  thence  proceeds 
in  the  manner  indicated  in  the  diagram,  ending  at  the  zero 
point  P,  when  the  last  installment  of  income  OP  is  received. 


FIG.  32. 

In  this  chapter  we  have  treated  income  as  accruing  dis- 
continuously ;  but  it  is  not  difficult,  in  accordance  with  the 
suggestions  made  in  a  previous  chapter,  to  extend  the  prin- 
ciples to  apply  to  the  continuous  case.  It  would  also 
be  possible,  were  it  worth  while,  to  exhibit,  by  means 
of  similar  diagrammatic  representations,  numerous  proposi- 
tions other  than  those  already  noted.  Our  object,  however, 
has  not  been  to  exploit  the  diagrams,  but  merely  to  use  them 
for  a  running  epitome  of  the  general  relations  existing  be- 
tween capital  arid  income. 


CHAPTER  XVIII 

GENERAL    SUMMARY 
§1 

IT  has  been  the  endeavor  in  the  preceding  chapters  to 
give  a  definite  picture  of  the  mass  of  capital  and  its  services 
to  man.  In  such  a  picture  we  see  man  standing  in  the 
midst  of  a  physical  universe,  the  events  of  which  affect 
his  life.  Over  many  of  these  events  he  can  exercise  no 
control  or  selection  ;  these  constitute  his  natural  environ- 
ment. Over  others  he  exercises  selection  and  control  by 
assuming  dominion  over  part  of  the  physical  universe, 
and  fashioning  it  in  new  shapes  to  suit  his  needs.  The 
parts  of  the  material  world  which  he  thus  appropriates 
constitute  wealth,  whether  they  remain  in  their  natural 
state  or  are  " worked  up"  by  him  into  products  to  render 
them  more  adapted  to  his  needs.  This  mass  of  instru- 
ments will  consist,  first,  of  the  appropriated  parts  of  the 
surface  of  the  earth,  of  the  buildings  and  structures 
attached  to  the  soil,  and  of  the  movable  objects  or  " com- 
modities" which  man  possesses  and  stores  in  the  buildings 
upon  the  earth ;  and,  secondly,  of  the  persons  of  the 
human  population  itself,  —  for  these,  though  they  are  al-o 
the  abode  of  the  owner  of  wealth,  are  themselves  objects 
owned. 

This  mass  of  instruments  serves  man's  purpose  in  so  far 
as  its  possession  enables  him  to  modify  the  stream  of  his- 
torical events.  By  means  of  land  and  the  modifications 
which  he  makes  upon  it  he  is  enabled  to  increase  and  im- 
prove the  growth  of  the  vegetable  and  animal  kingdoms 

323 


324  NATURE    OF   CAPITAL   AND    INCOME      [CHAP.  XVIII 

in  such  a  way  as  to  supply  him  with  food  and  the  mate- 
rials for  constructing  other  instruments.  By  means  of 
dwellings  and  other  buildings  he  is  enabled  to  divert  the 
elements  from  contact  with  his  body  and  with  the  objects 
of  wealth  which  he  stores  in  them.  By  means  of  machin- 
ery, tools,  and  other  instruments  of  production,  he  is 
enabled  to  fashion  new  instruments  to  add  to  his  stocks 
or  to  take  the  place  of  those  destroyed  or  worn  out.  By 
means  of  the  final  finished  products  which  minister  to  his 
more  immediate  enjoyments,  such,  for  instance,  as  food, 
clothing,  books,  ornaments,  he  is  enabled  to  consummate 
the  objects  for  which  the  entire  mass  of  wealth  is  produced 
and  kept  in  existence,  namely,  the  satisfaction  of  his  de- 
sires, whether  these  be  for  the  necessities,  the  luxuries,  the 
comforts,  or  the  amusements  of  life.  In  these  and  other 
ways  the  stock  of  wealth  will  modify  the  course  of  natural 
events  in  ways  more  or  less  agreeable  to  the  owner.  These 
changes  in  the  historical  stream  of  events  which  occur  by 
means  of  wealth  constitute  what  have  been  called  the  serv- 
ices of  wealth. 

In  our  picture,  therefore,  we  observe  (1)  a  stock  of  instru- 
ments existing  at  an  instant  of  time,  and  (2)  a  stream  of 
services  through  time,  flowing  from  this  stock  of  wealth. 
The  stock  of  wealth  is  called  capital,  and  its  stream  of  serv- 
ices is  called  income.  The  income  is  the  more  important 
concept  of  the  two,  for  the  capital  exists  merely  for  the 
sake  of  the  income,  and  the  ownership  of  the  capital  has  no 
other  significance  than  the  ownership  of  possible  income 
from  that  capital.  The  division  of  income  between  differ- 
ent owners  constitutes  in  reality  a  division  of  ownership 
of  the  capital  which  bears  the  income,  and  the  individual 
shares  constitute  what  are  called  property  rights. 

§<-> 
2 

From  this  it  is  apparent  that  property  rights  and  wealth 
go  side  by  side,  and  that  neither  can  exist  without  the  other, 


Six.  '-']  GKNKRAL   SUMMARY  325 

property  signifying  merely  the  sharing  of  wealth  among 
individuals.  When  we  piece  together  these  shares,  we  ob- 
tain the  ownership  of  all  wealth.  In  like  manner,  the  value 
of  the  entire  mass  of  wealth  must  be  taken  to  mean  simply 
the  sum  of  the  values  of  the  individual  shares  of  this  owner- 
ship. When  we  attempt  to  reach  this  total  by  combining 
the  shares  of  individuals,  we  do  so  by  making  a  careful 
record  of  all  "capital  accounts."  In  such  a  record  we  find 
that  many  items  occur  in  pairs, — negative  items  of 
property  or  " liabilities"  in  one  account  and  positive  items 
or  "assets"  in  another.  By  this  pairing  of  items,  there 
will  be  left  as  the  final  sum  of  property  value  the 
value  of  the  entire  stock  of  physical  instruments. 

Of  the  services  which  flow  from  the  stock  of  capital, 
it  has  been  seen  that  the  great  majority  consist  merely 
of  "interactions"  between  one  category  of  capital  and 
another.  All  that  is  accomplished  by  most  instruments 
of  capital  is  to  hand  over  something  to  other  instruments  of 
capital.  The  great  mass  of  capital — lands,  warehouses,  rail- 
roads, machinery,  ships,  etc. — exists  either  for  "transpor- 
tation," that  is,  for  changing  the  position  of  wealth  from 
one  place  to  another;  or  for  "production,"  that  is,  for  chang- 
ing wealth  from  one  state  or  form  to  another;  or  finally 
for  exchange,  the  mutual  transfer  of  rights  to  wealth.  In 
every  such  operation,  the  instruments  which  have  wrought 
the  change  are  said  to  have  rendered  a  service;  and  in  the 
income  account  these  instruments  are  credited  with  the 
value  of  such  services;  while  the  instruments  which  receive 
the  services,  and  are  thus  improved  in  position  or  condi- 
tion, are  said  to  have  rendered  a  disservice  and  are  at 
the  same  time  debited  with  exactly  the  same  item.  When 
we  thus  come  to  put  together  the  entire  total  of  income, 
all  such  pairs  of  items  or  "interactions"'  cancel.  These 
double-faced  events  or  interactions  constitute  the  over- 
whelming mass  of  items  in  the  actual  inventory  of  income 
which  enter  into  the  accounts  of  business  men.  Out  of 


326  NATURE    OF   CAPITAL   AND    INCOME          [CiiAP.  XVIII 

this  fact,  combined  with  the  fact  that  every  "  transaction  " 
is  also  double-faced,  grows,  as  we  have  seen,  the  entire 
theory  of  double-entry  bookkeeping. 

Out  of  the  entire  mass  of  instruments  thus  acting  and 
reacting  upon  each  other,  there  finally  emerges  an  uncan- 
celed  or  net  income  which  does  not  represent  a  mere  transfer 
from  one  category  to  another  within  the  mass,  but  an  actual 
contribution  issuing  from  the  mass  to  the  benefit  of  man, 
the  owner.  These  final  elements  are  his  real  income.  In 
the  last  analysis  they  consist  purely  of  subjective  or  psychic 
satisfactions;  that  is,  of  conscious  desirable  experiences. 

§3 

But  these  desirable  mental  experiences  occur  at  the  sacri- 
fice of  certain  undesirable  ones,  namely,  of  efforts.  The 
subjective  efforts  put  forth  for  the  sake  of  subjective  satis- 
factions constitute  the  net  or  uncanceled  elements  of  outgo. 
Thus  we  see  that,  side  by  side  with  the  objective  income 
and  outgo  stream,  and  as  the  final  result  of  that  stream,  there 
exists  its  subjective  counterpart,  namely,  the  stream  of  ef- 
forts and  satisfactions.  In  the  same  way,  there  exists,  side  by 
side  with  the  objective  mass  of  capital,  the  subjective  esteem 
in  which  this  capital  is  held,  namely,  what  we  have  called 
its  desirability,  or  utility.  If  efforts  and  satisfactions  are 
called  subjective  income,  desirability  or  utility  should  be 
called  subjective  capital.  The  same  antithesis  of  time 
applies  to  the  subjective  as  to  the  objective;  desirability 
is  a  state  of  mind  at  an  instant  of  time;  efforts  and  satis- 
factions are  experiences  through  a  period  of  time.  Desir- 
ability stands  for  anticipated  efforts  and  satisfactions,  just 
as  objective  capital  stands  for  anticipated  services.  We 
thus  see  in  the  mind  of  man  a  microcosm  of  the  objective 
economic  world,  consisting  of  desires,  efforts,  and  satis- 
factions, corresponding  respectively  in  the  objective  world 
to  capital,  outgo,  and  income. 


SEC.  4]  GENERAL    SUMMARY  327 

§4 

For  convenience  we  have  used  the  term  "goods"  to  com- 
prise any  one  or  all  of  the  three  categories,  —  wealth,  prop- 
erty, and  services.  It  has  been  seen  that  any  two  goods 
may  be  compared  in  respect  to  desirability,  and  if  the 
marginal  increments  of  two  groups  of  goods  are  equally 
desirable,  those  groups  are  equivalent  in  value.  The  inter- 
equivalence  of  goods  in  this  sense  may  be  measured  by  ex- 
pressing all  goods  in  terms  of  any  one  good,  as,  for  instance, 
money.  When  the  various  goods  are  thus  converted  into 
a  common  standard,  we  have  a  new  sense  both  for  capital 
and  income.  Capital,  instead  of  consisting  of  a  miscellane- 
ous mass  of  wealth  or  property  rights,  is  now  taken  in  the 
sense  of  capital-value;  and  income,  instead  of  consisting 
of  a  miscellaneous  stream  of  services,  some  final  and  some 
intermediate,  some  objective  and  some  subjective,  will 
consist  of  a  single  homogeneous  element,  income-value. 

It  is  to  the  relation  between  capital  and  income  in  the 
value  sense  that  our  attention  throughout  this  book  has 
been  chiefly  devoted.  It  has  been  noted  that  the  relation 
between  capital  and  income,  taken  in  the  value  sense,  is 
profoundly  different  from  the  relation  between  capital  and 
income  when  either  or  both  are  measured  in  their  various 
individual  units.  When  capital  and  value  are  measured 
as  "quantities,"  capital  may  be  said  to  produce  income; 
but  when  they  are  measured  in  "values,"  we  find  that  it 
is  necessary  to  reverse  this  statement,  and  to  say  that  in- 
come produces  capital.  The  manner  in  which  capital- 
value  is  produced  from  income- value  is  by  discounting,  and 
this  is  done  by  means  of  a  rate  of  interest,  due  attention 
being  given  to  the  fact  that  future  income  is  always  subject 
more  or  less  to  the  element  of  chance.  As  a  consequence 
of  this  fundamental  discount  relation,  it  follows  that  the 
value  of  capital  rises  as  future  income  approaches,  and  falls 
as  that  income  is  reached  and  passed.  It  rises  or  falls  with 


328  NATURE    OF   CAPITAL   AND    INCOME      [CHAP.  XVIII 

each  change  in  the  rate  of  interest  employed  in  the  discount 
process,  and  with  each  change  in  the  estimate  of  the  chance 
element.  If  the  alternate  rise  and  fall  in  the  value  of  capital 
are  rhythmic  and  even,  the  capital  will  recur  to  a  con- 
stant level,  and  the  income  in  this  case  is  said  to  be  the 
earnings  of  capital.  The  earnings  of  capital  constitute  a 
standard  with  respect  to  which  the  actual  income  in  any 
case  may  be  compared.  If  the  actual  income  exceeds  the 
standard  income,  there  will  be  a  depreciation  of  capital, 
which  may  be  made  good,  however,  by  paying  back  the 
excess  into  another  fund  of  capital  called  the  depreciation 
fund.  If,  on  the  contrary,  the  earnings  exceed  the  actual 
income,  the  excess  will  constitute  savings,  and  will  accumu- 
late and  be  added  to  the  capital. 

§5 

To  describe  in  a  few  words  the  nature  of  capital  and 
income,  wTe  may  say  that  those  parts  of  the  material 
universe  which  at  any  time  are  under  the  dominion  of 
man  constitute  his  capital  wealth ;  its  ownership,  his  capital 
property;  its  value,  his  capital-value;  its  desirability,  his 
subjective  capital.  But  capital  in  any  of  these  senses 
stands  for  anticipated  income,  which  consists  of  a  stream 
of  services  or  its  value.  When  values  are  considered,  the 
causal  relation  is  not  from  capital  to  income,  but  from 
income  to  capital;  not  from  present  to  future,  but  from 
future  to  present ;  in  other  words,  the  value  of  capital  is 
the  discounted  value  of  the  expected  income.  The  fluctu- 
ations of  this  capital-value  will,  chance  aside,  be  equal  and 
opposite  to  the  deviations  of  '''income"  from  "earnings," 
whereas,  when  the  influence  of  chance  is  included,  there 
will  be  in  addition  to  these  fluctuations  still  others  which 
mirror  the  successive  changes  in  the  outlook  for  future 
income. 


GLOSSARY 
A   SUMMARY  OF  THE  DEFINITIONS  USED  IN  THIS  BOOK 

Amortization  fund.  —  (Sec  Fund,  depreciation.) 

Amount.  —  The  amount  of  any  given  sum  at  a  given  time  is  its 

equivalent  at  a  later  time.     Ch.  XIII,  §  1. 

Assets  of  a  person.  —  His  property-rights,  including    both    those 

which  make    good    his   liabilities   and    those,    if   any,    which 

are  in  excess  of  and  free  from  any  liability.     (Syn.  Resources.) 

Ch.  V,  §  1. 

Balance  sheet.  —  A  statement  of   a  person's  assets  and  liabilities. 

(Syn.  Capital  account.)     Ch.  V,  §  1. 
Basis.  —  The  rate  of  interest  yielded  by  a  security  when  sold  at  a 

specified  price.     Ch.  XVI,  §  9. 
commercial,    of   a   security.  —  The    basis    corresponding   to    the 

commercial  value  of  the  security.     Ch.  XVI,  §  8. 
mathematical,   of  a  security.  —  The  basis  corresponding  to  the 

mathematical  value  of  the  security.     Ch.  XVI,  §  8. 
riskier,  of  a  security.  —  The  basis  corresponding  to  the  riskless 

value  of  the  security.     Ch.  XVI,  §  8. 
Capital.  —  Abbreviation    for    Capital    goods,    and    Capital    value. 

Ch.  V,  §  1. 

account.  —  (See  Balance  sheet.)     Ch.  V,  §  1. 
balance.  —  The  difference  between  the  value  of  the  assets  in  a 
balance  sheet  and  of  the  liabilities.     (Syn.  Net  capital.) 

The  capital  balance  is  measured  in  three  different  ways: 
as  the  nominal  capital  (or  capitalization),  the  book  value,  and 
the  market  value  of  the  rights  of  the  shareholders  or  those 
whose  capital  account  is  considered.  Ch.  V,  §  1. 
book  value  of.  —  The  sum  of  the  capital,  surplus,  and  un- 
divided profits,  i.e.  the  difference  in  value  at  any  time  between 
the  assets  and  liabilities  according  to  the  entries  in  the  capital 
account.  Ch.  V,  §  4. 

goods.  —  Capital-wealth  or  capital-property.     Ch.  V,  §  1. 
as  market  value  of  shares.  —  The    market  value  of    the   share- 
holders' rights  in  a  concern.     Ch.  V,  §  4. 
instruments.  —  (See  Capital  uralth.) 

329 


330  NATURE   OF   CAPITAL   AND   INCOME 

Capital,  net.  —  (See  Capital  balance.)     Ch.  V,  §  3. 

nominal.  —  The  par  or  face  value  of  the  shares  in  a  joint  stock 
company,  and  hence  also  the  original  book  value  of  the  differ- 
ence between  assets  and  liabilities.  Ch.  V,  §  2. 

original.  —  The  capital  when  the  capital  account  is  first  opened. 
It  may  be  measured  in  two  different  ways,  as  nominal  capital 
and  paid-up  capital.  Ch.  IV,  §  4. 

paid-up.  —  The  amount  of  original  capital  of  a  concern  actually 
paid  in  by  the  shareholders.  Ch.  IV,  §  4. 

property.  —  A  stock  (or  fund)  of  property  existing  at  an  instant 
of  time.  Ch.  V,  §  1. 

wealth.  —  A  stock  (or  fund)  of  wealth  existing  at  an  instant  of 
time.  (Syn.  Capital  instruments.)  Ch.  V,  §  1. 

value.  —  The  value  of  a  stock  of  wealth  or  property  at  an  instant. 
It  is  found  by  discounting  (or  ''capitalizing")  the  value  of  the 
income  expected  from  the  wealth  or  property.  Ch.  V,  §  1. 
Capitalization.  —  A.  The  process  of  discounting  by  which  ex- 
pected income  is  translated  into  present  capital- value.  Usually 
employed  only  when  the  income  is  considered  uniform  and 
perpetual,  in  which  case  capitalization  consists  in  dividing  the 
rate  of  income  per  annum  by  the  rate  of  interest.  Ch.  IV,  §  6 ; 
Ch.  XIII,  §  1. 

B.   The  nominal  capital  of  a  joint  stock  company.  Ch.  V,  §  4. 

rate  of.  —  The  reciprocal  of  the  rate  of  interest.     (Theoretically 
also  the  reciprocal  of  the  rate  of  discount.     Practically  this 
meaning  is  never  used.) 
Capitalize.  —  To   capitalize   income   is   to   find   the   capital-value 

equivalent  to  that  income.     Ch.  IV,  §  6;   Ch.  XIII,  §  1. 
Caution,  coefficient  of.  —  The  ratio  of  commercial  value  to  mathemat- 
ical value.     Ch.  XVI,  §  6. 

Chance,  of  any  event.  —  The  ratio  of  the  number  of  cases  in  which 
that  event  may  occur  to  the  total  possible  number  of  cases, 
when  all  the  cases  are  equally  probable.  Any  two  cases  are 
equally  probable  (to  any  particular  person  at  any  particular 
time)  if  the  person  has  no  inclination  to  believe  one  rather  than 
the  other  to  be  true.  Ch.  XVI,  §  2.  (Syn.  Probability.) 

commercial  value  of.  —  The  value  which  the  chance  will  actually 
command  in  the  market.  It  is  equal  to  the  mathematical 
value  multiplied  by  the  coefficient  of  caution,  Ch.  XVI,  §  6. 

mathematical  value  of.  —  The  product  of  the  value  of  the  prize 
at  stake  multiplied  by  the  chance  of  winning  it.     Ch.  XVI,  §  5. 
Coefficient,  of  caution.  —  The  ratio  of  commercial  value  to  mathe- 
matical value.     Ch.  XVI,   §  6. 


SUMMARY   OF   DEFINITIONS  331 

Coefficient,  of  probability.  —  The  ratio  of  mathematical  value  to  risk- 
less  value.  Ch.  XVI,  §  0. 

of  risk.  —  The  ratio  of  commercial  value  to  riskleas  value ;  hence 
the  product  of  the  coefficient  of  caution  multiplied  by  the 
coefficient  of  probability.  Ch.  XVI,  §  6. 

Commercial  basis.  —  (See   Basis,   commercial.) 

value  of  a  chance.  —  (See  Chance,  commercial  value  of.) 

Commodities.  —  Movable  instruments  not  human  beings.     Ch.  I,  §  2. 

Consumption.  —  (See  Services,  enjoyable  objective.) 

Couple.  —  A  liability  to  a  debtor  and  its  counterpart  asset  to  the 
creditor.  Or  the  service  of  one  instrument  acting  on  another 
and  the  counterpart  disservice  of  the  second  acted  on  by  the 
first.  Ch.  VI,  §  1 ;  Ch.  IX,  §  2. 

Coupled  services.  —  (See  Couple,  Interaction.) 

Depreciation  fund.  —  (See  Fund,  depreciation.) 

Desirability  of  goods  (wealth,  property,  or  services). — The  inten- 
sity of  desire,  for  those  goods,  of  a  particular  individual  at  a 
particular  time  under  particular  circumstances.  (Syn.  Utility.) 
Ch.  Ill,  §  2. 

marginal  —  of  a  specified  aggregate  of  goods.  —  Approximate 
definition :  The  desirability  of  one  unit  more  or  less  of  that 
aggregate,  or  the  difference  between  the  desirability  of  that 
aggregate  and  another  aggregate  one  unit  larger  or  smaller. 
Ch.  Ill,  §  4. 

Exact  definition :  The  limit  of  the  ratio  of  the  increment 
(or  decrement)  of  desirability  to  the  increment  (or  decrement) 
of  the  aggregate  when  the  last-named  increment  (or  decrement) 
approaches  zero.  (Syn.  Marginal  utility.)  Appendix  to  Ch. 
Ill,  §  1. 

progressive  marginal  —  of  a  specified  aggregate  of  goods.  —  The 
desirability  of  one  unit  more  of  that  aggregate.     (Syn.  Pro- 
gressive marginal  utility.)     Appendix  to  Ch.  Ill,  §  1. 
regressive  marginal  —  of  a  specified  aggregate  of  goods.  —  The  de- 
sirability of  one  unit  less  of  that  aggregate.     (Syn.  Regressive 
marginal  utility.)     Appendix  to  Ch.  Ill,  §  1. 
total  —  of  an  aggregate  of  goods. — The  difference  between  the 
desirability  of  goods  which  include  and  of  those  which  exclude 
that  aggregate.     (Syn.  Total  utility.)     Ch.  Ill,  §  4. 

Dimension.  —  The  kind  or  species  of  any  magnitude  as  indicated 
by  its  measurement  in  terms  of  other  magnitudes.  Appendix 
to  Ch.  I. 

Discount  curve.  —  A  curve  so  constructed  that,  if  one  of  its  ordinates 
represents  any  given  sum,  any  later  ordinate  will  represent  the 


332  NATURE    OF   CAPITAL   AND   INCOME 

"amount"  of  that  sum  at  a  time  later  by  an  interval  repre- 
sented by  the  horizontal  distance  between  the  ordinates ;  and 
which  is  consequently  also  such  that  any  earlier  ordinate  will 
represent  the  "present  value"  of  that  sum  at  a  time  earlier 
by  an  interval  represented  by  the  horizontal  distance  between 
the  ordinates.  Ch.  XIII,  §  1. 

Discount,  rate  of.  —  The  deficiency  below  unity  of  the  ratio  of 
exchange  between  the  values  of  present  and  future  goods,  taken 
in  relation  to  the  time  interval  between  the  two  sets  of  goods. 
Ch.  XII,  §  7. 

The  rate  of  discount  may,  like  the  rate  of  interest,  be  reck- 
oned annually,  semi-annually,  quarterly,  or  continuously.  (It 
may  also,  theoretically,  be  taken  in  the  price  sense  as  well  as 
in  the  sense  above,  but  practically  never  is.) 
total.  —  The  difference  between  any  sum  and  its  discounted  or 
present  value. 

Discounted  value.  —  (See  Value,  present.} 

Disservice.  —  A  negative  service.  An  instrument  renders  a  dis- 
service when,  by  its  means,  an  undesirable  event  is  promoted 
or  a  desirable  event  prevented.  Ch.  II,  §  2;  Ch.  VIII,  §  1. 

Disutility.  —  Negative  utility.  (Syn.  Undesir ability.}  Ch.  Ill, 
§2. 

Earnings.  —  (See  Income,  earned.} 

Exchange.  —  The  mutual  and  voluntary  transfer  of  goods  (wealth, 
property,  or  services)  between  two  owners,  each  transfer  being 
in  consideration  of  the  other.  Ch.  I,  §  4;  Ch.  II,  §  3. 

Expense.  —  Outgo  in  the  form  of  money-spending.     Ch.  VIII,  §  1. 

Flow.  —  The  quantity  of  any  specified  thing  undergoing  any  speci- 
fied change  during  any  specified  period  of  time.     Ch.  IV,  §  1. 
rate  of.  —  The  ratio  of  a  flow  to  its  duration.     Ch.  IV,  §  1. 

Fund.  —  A  stock  of  wealth  or  property  or  its  value.     Ch.  IV,  §  1. 
amortization.  —  (See  Fund,  depreciation.} 

depreciation.  —  A  fund  formed  by  accumulating  that  part  of 
income  which  must  be  turned  back  into  capital  to  maintain  the 
capital-value  intact.  It  may  also  be  defined  as  formed  from 
the  difference  between  real  income  and  earnings,  when  that 
difference  is  accumulated. 

If  the  income  is  uniform  and  runs  only  for  a  fixed  term,  the 
depreciation  fund  may  also  be  defined  as  formed  from  a  suc- 
cession of  equal  payments  out  of  income,  such  that  if  each  be 
accumulated  at  compound  interest,  the  total  will  be  equal  to  the 
original  capital  at  the  end  of  the  income  term.  (Syn.  Amorti- 
zation fund.)  Ch.  XIV,  §  6. 


SUMMARY   OF   DEFINITIONS  333 

Fund,  sinking.  —  A  fund  formed  by  accumulating  the  difference 
between  actual  income  and  a  terminable  annuity  which  has 
the  same  present  worth. 

As  applied  to  bonded  debts  it  may  also  be  defined  as 
formed  by  accumulating  an  annual  sum  such  that  its  amount 
will  just  suffice  to  equal  (or  extinguish)  a  given  sum  at  the 
end  of  a  given  period.  Ch.  XIV.  §  7. 

Income.  —  Abbreviation  for  Income  services  and  Income  value. 
Ch.  VIII,  §  1. 

account.  —  Statement  of  specified  income  and  outgo,  whether  from 
capital  or  to  a  person. 

earned,  by  any  capital.  —  Income  realized  plus  appreciation 
of  the  capital  (or  minus  its  depreciation).  I.e.  that  income 
which  a  given  capital  can  yield  without  alteration  in  its  value. 
If  interest  be  assumed  invariable  and  all  future  income  fore- 
known, this  definition  is  equivalent  to  another,  viz.  the  uniform 
and  perpetual  income  which  a  given  capital  might  yield ; 
but  the  equivalence  ceases  if  interest  varies  (see  Appendix  to 
Ch.  XIV,  §  1)  or  if  future  income  is  unknown.  (Syn.  Earnings, 
Standard  income.)  Ch.  XIV,  §  4. 

enjoyable.  —  Income  which  consists  of  enjoyable  services.  Ch. 
VII,  §  6. 

gross.  —  Sum  of  all  positive  income  elements.     Ch.  VII,  §  1. 

individual.  —  The  income  from  the  entire  capital  of  an  individual. 
Ch.  VII,  §  7. 

money.  —  Income  which  consists  of  the  receipt  of  money. 
Ch.  VII,  §  7 ;  Ch.  IX,  §  5. 

natural.  —  Income  which  consists  of  services  not  obtained  by 
exchange.  Ch.  VII,  §  7 ;  Ch.  IX,  §  5. 

net.  —  The  difference  between  gross  income  and  outgo.  Ch.  VIII,  §  1. 

psychic.  —  Agreeable  conscious  experiences.  (Syn.  Subjective 
income.)  Ch.  X,  §  3. 

realized,  from  any  capital  —  Actual  income,  i.e.  the  value  of  its 
actual  services. 

services,  of  any  capital.  —  The  flow  of  services  from  that  capital 
through  a  period  of  time.  Ch.  VIII,  §  1. 

social.  —  The  income  from  the  entire  capital  of  the  society. 
Ch.  VII,  §  7. 

standard.  —  (See  Income,  earned.) 

subjective.  —  (See  Income,  psychic.) 

value,    from   any   capital.  —  The    value   of   its   income-services. 

Ch.  VIII,  §  1. 
Instrument. — An  individual  article  of  wealth.     Ch.  I,  §  1. 


334  NATURE   OF   CAPITAL   AND   INCOME 

Interaction.  —  An  event  which  is  a  service  of  one  capital  and  at  the 
same  time  a  disservice  of  another.  (Syn.  Interacting  service, 
Intermediate  service,  Preparatory  service,  Coupled  service.) 
Ch.  IX,  §  2. 

Interacting  services.  —  (See  Interaction.) 
Intermediate  services.  —  (See  Interaction.) 
Interest.  —  The  product  of  the  rate  of  interest  multiplied  by  the 

capital-value.     Ch.  XIV,  §  4. 

nominal.  —  The  stipulated  annual  payments  on  a  bond  or  note 
nominally  (but  not  always  in  fact)  equal  to  the  interest  on  the 
"principal."  Ch.  XIII,  §  7. 

rate  of.  —  Many  meanings  are  given  below.  The  standard  mean- 
ing used  in  this  book  is  that  called  "rate  of  interest  in  the  pre- 
mium sense  reckoned  annually." 

rate  of.  —  In  the  price  sense :  The  ratio  between  the  annual  rate 
of  a  perpetual  annuity  and  the  equivalent  capital-value. 
Ch.  XII,  §  2. 

The  rate  of  interest  is  said  to  be  reckoned  annually  if  the 
annuity  is  payable  in  annual  installments ;  it  is  said  to  be 
reckoned  semi-annually,  if  the  annuity  is  payable  in  semi- 
annual installments ;  quarterly,  if  in  quarterly  installments ; 
continuously,  if  payable  continuously. 

rate  of.  —  In  the  premium  sense:  The  excess  above  unity  of  the 
rate  of  exchange  between  the  values  of  future  and  present  goods 
taken  in  relation  to  the"  time  interval  between  the  two  sets  of 
goods.  (Syn.  rate  of  interest  in  the  agio  sense.)  Ch.  XII,  §  4. 
The  rate  of  interest  is  said  to  be  reckoned  annually  if  the  two 
sets  of  goods  are  one  year  apart.  This  is  the  standard  meaning 
of  the  "rate  of  interest"  as  used  in  this  book.  It  is  said  to  be 
reckoned  semi-annually,  if  they  are  a  half-year  apart ;  quar- 
terly, if  three  months  apart ;  continuously,  if  infinitesimally 
apart. 

rate  of.  —  In  agio  sense :    (See  in  premium  sense.) 
rate   of.  —  Reckoned  annually,   semi-annually,   quarterly,  contin- 
uously: (See  under  rate  of  interest  in  price  sense  and  rate  of 
interest  in  premium  sense.) 
total. — The   difference   between   any   sum   and   its   "amount." 

Appendix  to  Ch.  XIII,  §  7. 

Labor.  —  Outgo  in  the  form  of  human  exertion.     Ch.  X,  §  6. 
Land.  —  Wealth  which  is  part  of  the  earth's  surface.     Ch.  I,  §  2. 
improvements.  —  Wealth  constructed  upon  and  attached  to  land, 

Ch.  I,  §  2. 
Liabilities  of  a  person.  —  Amount  of  obligations  due  others.  Ch.  V,  §  1 . 


SUMMARY   OF   DEFINITIONS  335 

Mathematical  basis.  —  (Sec  Basis,  mathematical.) 

value  of  a  chance.  —  (Sec  Chance.) 

Method,  of  balances.  —  The  method  of    summing  capital-    or   in- 
come-accounts which  consists   in  first   deducting  the  sum  of 
the  negative  items  in  each  from  the  sum  of  the  positive  items, 
and  then  adding  the  "balances"  thus  obtained.     Ch.  IX,  §  2. 
of  couples.  —  The  method  of  summing  capital  accounts  and  income 
accounts   which    consists    in    canceling    out    the   "couples.' 
Ch.  IX,  §  2. 
Outgo.  —  Negative  income.     Ch.  VIII,  §  1. 

net. — Net  income,  when   negative.     Ch.  VIII,  §  1. 
Person.  —  Any  owner  of  property,  whether  real  or  fictitious.     Ch. 

II,  §3. 

fictitious.  —  An  imaginary  entity  (such  as  a  firm  or  corporation) 
regarded,  for  bookkeeping  purposes,  as  holding  property  for 
a  number  of  other  persons  (real  or  fictitious.)     Ch.  II,  §  2. 
real. —  An  owner  of  property  who  is  a  living  human  being. 
Price.  —  A  ratio  of  exchange.     Ch.  I,  §  4. 

money.  —  The  quotient  found  by  dividing  the  money  exchanged 
for  goods  by  the  quantity  of  the  goods  themselves.  Ch.  I, 
§4. 

Principal.  —  The  final  payment  on  a  bond  or  note,  supposed  to  be 
(but  not  always  in  fact)  equal  to  the  original  sum  "  lent." 
Ch.  XIII,  §  7. 

Preparatory  services.  —  (See  Interaction.) 
Probability.  —  See  Chance. 

coefficient  of.  —  The  ratio  of  mathematical  value  to  riskless  value. 

Ch.  XVI,  §  6. 

Production.  —  (See  Transformation.) 
Productive  process.  —  (See  Transformation.) 

Productivity,  physical.  —  The  ratio  of  the  quantity  of  services  of  cap- 
ital per  unit  of  time  to  the  quantity  of  the  capital.     Ch.  XI,  §  2. 
value.  —  The  ratio  of  the  value  of  services  of  capital  per  unit  of 

time  to  the  quantity  of  the  capital.     Ch.  XI,  §  2. 
Property  (or  property  rights).  —  Rights  to   the  chance  of  future 

services  of  wealth.     Ch.  II,  §  3. 
right,  complete. — The  exclusive  right  to  all  the  services  of  an 

instrument.     Ch.  II,  §  10. 

right,  partial.  —  The  right  to  part  of  the  services  of  an  instru- 
ment, other  parts  belonging  to  other  owners.     Ch.  II,  §  10. 
Purchase.  —  An  exchange  of  money  for  goods.     Ch.  I,  §  4. 
Real  estate.  —  Land  and  land  improvements.     Ch.  I,  §  2. 
Resources.  —  (See  Assets.) 


336  NATURE    OF   CAPITAL   AND   INCOME 

Return,  physical.  —  The  ratio  of  the  quantity  of  services  of  capital 

to  the  value  of  the  capital.     Ch.  XI,  §  2. 

value.  —  The  ratio  of  the  value  of  services  of  capital  to  the  value 
of  the  capital.    Ch.  XI,  §  2. 

Risk,  coefficient  of.  —  The  ratio  of  commercial  value  to  riskless  value. 
It  is  equal  to  the  product  of  the  coefficient  of  probability  multi- 
plied by  the  coefficient  of  caution.  Ch.  XVI,  §  6. 

Riskless  basis.  —  (See  Basis,  riskless.) 

value.  —  The  value  which  a  thing  would  have  if  risk  were  elimi- 
nated.    Ch.  XVI,  §  6. 
value  of  a  chance.  —  (See  Chance.) 

Sale.  —  An  exchange  of  goods  for  money.     Ch.  I,  §  4. 

Service.  —  An  instrument  renders  a  service  when,  by  its  means,  a 
desirable  event  is  promoted  or  an  undesirable  event  prevented. 
(Syn.  Use.)  Ch.  II,  §  2. 

Services,  coupled.  —  (See  Interaction.) 

enjoyable  objective.  —  Services  received  directly  by  human  beings, 
and  not  (like  interactions)  merely  received  for  human  beings 
by  other  objective   capital.      (Syn.  (not   well    chosen)   Con- 
sumption.)    Ch.  X,  §  1. 
intermediate.  —  (See  Interaction.) 
preparatory.  —  (See  Interaction.) 

Sinking  fund.  —  (See  Fund,  sinking.) 

Standard  income.  —  (See  Income,  earned.) 

Standardize.  —  To  standardize  a  given  income  is  to  convert  it  into 
its  equivalent  income  earned. 

Stock.  —  The  quantity  of  any  specified  thing  at  any  instant.  (Syn. 
Fund.)  Ch.  IV,  §  1. 

Transaction.  —  That  side  of  an  exchange  which  relates  to  one  of 
the  exchangers  ;  it  consists  of  two  items,  a  credit  and  a  debit. 
Ch.  IX,  §  9. 

Transfer.  —  An  interaction  which  is  a  change  of  ownership  of  wealth. 
Ch.  IX,  §  3. 

Transformation.  —  An  interaction  which  is  a  change  of  form  or 
condition  of  wealth.  (Syn.  Production,  Productive  process.) 
Ch.  IX,  §§  2,  3. 

Transportation.  —  An  interaction  which  is  a  change  of  place  or 
position  of  wealth.  Ch.  IX,  §§  2,  3. 

Undesir -ability.  —  Negative  desirability.  (Syn.  Disutility.)  Ch. 
Ill,  §  2. 

Utility  of  goods.     (See  Desirability.) 

Value.  —  The  value  of  goods  (wealth,  property,  or  services)  is  the 
product  of  their  quantity  multiplied  by  their  price.  Ch.  I,  §  6. 


SUMMARY    OF    DEFINITIONS  337 

Value,  commercial,  of  a  chance.  —  (See  Chance.) 
discounted.  —  (See  Value,  present.) 
mathematical,  of  a  chance.  —  (See  Chance.) 
money.  —  The  quantity  of  goods  multiplied  by  their  money  price. 

Ch.  I,  §  (5. 
present.  —  The  present  value  of  any  given  future  goods  is  the 

quantity  of  present  goods  which  will  exchange  for  those  future 

goods.     (Syn.  Present  worth,  Discounted  value.)    Ch.  XIII,  §  1. 
risklcss,  of  a  chance.  —  (See  Chance.) 
Wealth    (in    its    broader    sense).  —  Material     objects    owned     by 

human  beings.     Ch.  I,  §  1. 
(in   its   narrower  sense).  —  Material   objects  owned   by  human 

beings  and  external  to  their  owners.     Ch.  I,  §  2. 
article  of.  —  A  single  object  of  wealth.      (Syn.  Item  of  Wealth, 

Instrument.)     Ch.  I,  §  1. 

item  of.  —  (See  Wealth,  article  of.)     Ch.  I,  §  1. 
Worth,  present.  —  (See  Value,  present.) 


APPENDICES 

APPENDIX  TO  CHAPTER  I 
APPENDIX  TO  CHAPTER  III 
APPENDIX  TO  CHAPTER  VII 
APPENDIX  TO  CHAPTER  XI 
APPENDIX  TO  CHAPTER  XII 
APPENDIX  TO  CHAPTER  XIII 
APPENDIX  TO  CHAPTER  XIV 
APPENDIX  TO  CHAPTER  XVI 


APPENDIX  TO  CHAPTER  I 

§  1  (TO  CH.  I,  §  7) 
Dimensions  of  Wealth,  Price,  and  Value 

What  mathematicians  call  the  "dimension"  of  a  magnitude 
is  simply  its  species  or  kind,  as  indicated  by  its  measurement  in 
terms  of  other  magnitudes  of  the  same  or  different  kinds.  It 
is  expressed  mathematically  by  a  letter  or  letters.  Consider 
beef,  for  example.  If  b  represents  any  given  amount  of  beef, 
say  three  hundred  pounds,  this  letter  may  be  taken  to  indicate 

its  "dimension."  The  price  of  beef  in  terms  of  wheat  is  — , 
where  iv  stands  for  the  amount  of  wheat  exchangeable  for  an 
amount  b  of  beef.  The  expression  —  (or,  as  it  may  be  written, 

ivb~l)  thus  expresses  the  "dimension"  of  price.  It  matters 
not  what  particular  price  of  beef  in  terms  of  wheat  is  referred 
to.  Every  price  is  of  the  same  form  u-b~\  Finally,  the  di- 
mension of  the  "  value  "  of  the  beef  in  terms  of  wheat  is  w, 
for  this  value  is  the  product  of  the  amount  of  beef,  b,  by  its 

w    .      ,      ?/; 
price,    — ,  i.e.  bx—  =  w. 
b  b 

That  is,  the  dimension  of  beef  is  represented  by  b, 
its  price  by  P=—  =  u'b~l, 

its  value  "by  bp  =  b  —  —  w. 

b 

We  thus  have  a  different  dimension  for  each  of  the  three  differ- 
ent magnitudes.  This  fact  is  expressed  in  common  language, 
also.  We  measure  cloth  in  yards,  the  price  of  cloth  in  bushels 
per  yard,  the  value  of  cloth  simply  in  bushels.  Price  and  value 
differ  as  fundamentally  as  velocity  and  distance,  which  are 
measured  respectively  in  feet  per  second  and  plain  feet ;  or  as 

341 


342  NATURE   OF   CAPITAL   AND   INCOME 

density  and  weight,  which  are  expressed  in  pounds  per  cubic 
foot  and  simply  pounds. 

It  may  seem  at  first  that  these  distinctions  between  the 
dimension  of  price,  quantity,  and  value  are  somewhat  strained. 
It  may  be  claimed  that  price  is  simply  the  value  of  a  unit,  and 
that  value  is  simply  the  price  of  the  whole  quantity.  In  the 
same  way  it  is  sometimes  loosely  said  that  the  velocity  of  a 
moving  body  is  simply  the  distance  traversed  in  a  unit  of  time. 
It  is  quite  true,  of  course,  that  the  number  which  expresses 
the  value  of  a  unit  of  wealth  is  the  same  number  as  that  which 
expresses  the  price  per  unit.  It  is  likewise  true  that  the 
number  which  expresses  velocity  is  the  same  as  that  which  ex- 
presses the  distance  which  will  be  traversed  in  a  unit  of  time. 
Yet  velocity  is  not  distance,  and  no  more  is  price,  value;  although 
practically  where  the  wealth  under  consideration  is  or  may 
be  regarded  as  a  single  unit,  it  is  less  necessary  to  insist  on 
the  distinction  between  value  and  price.  If  the  price  of  a 
"  unique  "  is  $25  per  unit,  then  its  value  is  also  $25.  If  a  farm 
of  100  acres  has  a  value  of  $5000,  the  price  of  the  farm  as  a 
single  thing,  and  not  as  measured  in  acres,  is  $5000  per  farm. 
But  as  soon  as  we  have  to  deal  separately  with  a  single  unit 
and  a  number  of  units,  we  must  make  a  distinction  between 
price  and  value.  That  they  are  not  of  the  same  dimension  is 
clear  from  the  fact  that  the  number  expressing  the  price  of 
beef  in  terms  of  wheat  varies  with  both  the  unit  of  beef  and  of 
wheat,  while  the  number  expressing  the  value  of  beef  varies 
only  with  the  unit  of  wheat.  Thus,  if  the  quantities  of  beef  and 
wheat  which  exchange  for  each  other  are  300  pounds  and  60 
bushels  respectively,  the  price  and  value  of  the  beef  in  terms 
of  the  wheat  will  be 

price  of  the  beef,  \  bu.  per  Ib. 

value  of  the  beef,  60  bu. 

A  change  in  the  unit  of  measurement  for  beef  will  evidently 
affect  only  the  first  of  these  two  numbers.  Thus,  if  the  beef  is 
measured  in  ounces  (4800  oz.)  instead  of  in  pounds,  the  num- 
bers become : 

price  of  the  beef,  ^  bu.  per  oz. 

value  of  the  beef,  60  bu. 


APPKNDIX   TO   CHAPTER    I  343 

On  the  other  hand,  a  change  in  the  unit  for  measuring  the 
wheat  will  affect  both  numbers.  Thus,  if  wheat  is  meas- 
ured in  pecks  instead  of  in  bushels  (while  beef  is  still  meas- 
ured in  pounds),  the  numbers  representing  price  and  value  will 
change  from  ^  and  GO  to  £  and  240  respectively,  each  being 
magnified  fourfold. 

We  see  then  that  the  value  and  price  of  beef  are  similar 
in  that  they  are  similarly  affected  by  a  change  in  the  unit  of 
wheat  but  are  different  in  that  they  are  differently  affected  by 
a  change  in  the  unit  of  beef. 

It  may  aid  the  reader  who  is  unfamiliar  with  the  subject  of 
the  dimensionality  of  magnitudes  to  indicate  a  few  of  its  appli- 
cations to  physical  science.  If  I  is  taken  to  represent  the  di- 
mension of  length,  area  will  be  represented  by  P  and  volume 
by  P.  Consequently,  length,  area,  and  volume  are  said  to  be 
respectively  of  one,  two,  and  three  "dimensions,"  because 
1, 1-,  and  P,  which  represent  their  dimensionalities,  have  for  ex- 
ponents 1,  2,  and  3  respectively.  The  term  "dimension"  was 
originally  applied  simply  to  these  cases  of  length,  area,  and 
volume.  But  it  soon  came  to  be  extended  to  apply  to  every 
sort  of  mathematical  magnitude.  The  following  examples  are 
noted  without  comment  (I  stands  for  length,  m  for  mass,  and 
t  for  time)  :  — 

Velocity,  of  dimension  lt~l,  or  feet  per  sec. 
Acceleration,       "  lt~2,  or  feet  per  sec.  per  sec. 

Momentum,         "        mlt~l,  or  pounds  feet  per  sec. 
Force,  "        mlt~2,  or  pounds  feet  per  sec.  per  sec. 

Work,  "       mPt~2,  or  pounds  feet  feet  per  sec.  per  sec. 

Horse  power,      "       mFt~3,  or  pounds  feet  feet  per  sec.  per  sec. 

per  sec. 

To  illustrate  the  meaning  of  this  table,  we  observe  that  the 
number  which  represents  work  (or  energy)  would  be  affected 
by  a  change  in  the  units  of  mass,  length,  and  time,  as  follows  : 
Halving  the  unit  of  mass  (so  that  the  number  representing  any 
mass  would  be  doubled)  would  double  the  number  representing 
the  work ;  halving  the  unit  of  length  (so  that  the  number  rep- 
resenting any  given  length  would  be  doubled)  would  quadru- 
ple the  number  representing  work ;  halving  the  unit  of  time 


344  NATURE   OF   CAPITAL   AND   INCOME 

(so  that  the  number  representing  any  given  time  would  be 
doubled)  would  quarter  the  number  representing  the  unit  of 
work. 

The  idea  of  "  dimension  "  and  its  mode  of  representation  are 
important  subjects,  for  a  fuller  treatment  of  which  the  reader 
is  referred  to  the  article  on  the  subject  in  Palgrave's  Dictionary 
of  Political  Economy,  as  well  as  for  its  more  general  applica- 
tions to  J.  D.  Everett's  C.G.S.  System  of  Units,  1891. 

APPENDIX  TO  CHAPTER  III 

§  1  (TO  CH.  Ill,  §  4) 
Definition  of  Marginal   Desirability 

To  express  mathematically  the  marginal  utility  or  desirabil- 
ity of  any  group  of  goods,  let  A#  represent  any  increment  of 
goods  measured  in  any  specified  unit,  and  Au  the  desirability 
of  that  increment.  For  instance,  if  reference  is  had  to  a  bin  of 
coal  containing  15  tons,  and  if  Ao;  represents  an  increment 
of  3  tons,  At*  will  mean  the  desirability  of  those  3  tons,  so 

that  —  will  represent  the  average  desirability  per  ton  of  3  ad- 
ditional tons.  If  we  suppose  the  increment  Ace  to  be  succes- 
sively decreased  to  2  tons,  1  ton,  \  ton,  and  so  on  indefinitely, 

approaching  zero  as  a  limit,  the  expression  —  will  mean  suc- 

A# 

cessively  the  average  desirability  per  ton  of  2  additional  tons, 
the  desirability  of  1  additional  ton,  the  desirability  per  ton  of 
\  an  additional  ton  (i.e.  twice  the  desirability  of  that  addi- 
tional half  ton),  the  desirability  per  ton  of  \  an  additional  ton 
(i.e.  four  times  the  desirability  of  an  additional  -\  of  a  ton), 
etc.  The  limit  of  this  series  will  be  the  desirability  per  ton  of 
an  infinitesimal  increment  of  coal,  and  may  be  expressed  by 

the  fraction  — .     This,  which  is,  as  mathematicians  say,  the 
dx 

differential  quotient  of  desirability,  will,  assuming  continuity, 
have  the  same  value  if,  in  place  of  the  increment,  a  decrement 
were  considered;  that  is,  if  instead  of  supposing  the  owner  of 
the  15  tons  to  add  3  tons,  we  suppose  him  to  subtract  3  tons. 


APPENDIX    TO    CHAPTER    VII  345 

Then  —  would  represent  the  average  desirability  per  ton  of 

Ax 

this  3  tons  subtracted,  which  would  evidently  be  somewhat 
greater  than  the  desirability  per  ton  of  3  additional  tons. 
But  when  we  substitute  for  3  tons,  the  smaller  magnitudes 

2  tons,  1  ton,  ^  ton,  ^  ton,  etc.,  the  resulting  value  of  — -,  or  the 

l\Ju 

desirability  per  ton  of  this  constantly  lessening  decrement,  will 
become  equal,  at  the  limit,  to  the  desirability  per  ton  of  the 

constantly  lessening  increment.     The  limit  of  —  is  expressed 

A«C 

— .  The  expression  —  indicates  more  exactly  than  could  be 
cix  (tx 

indicated  in  the  text  the  true  meaning  of  marginal  desir- 
ability, and  when  the  article  may  be  indefinitely  subdivided, 
the  marginal  desirability  is  the  same  whether  reckoned 
by  increments  or  decrements.  Practically,  however,  such 
mathematical  subdivision  does  not  always  apply,  and  it  may 
even  happen  that  the  desirability  of  one  unit  more  may  be 
materially  different  from  the  desirability  of  one  unit  less.  For 
instance,  the  owner  of  one  piano  may  esteem  it  very  highly, 
but  a  second  piano  would  have  almost  no  desirability.  Here 
the  desirability  of  one  unit  less  is  far  greater  than  the  desir- 
ability of  one  unit  more,  owing  to  the  fact  that  the  piano  is  an 
indivisible  unit,  and  we  can  consider  no  increments  or  decre- 
ments except  of  whole  pianos.  In  this  case  instead  of  one 
marginal  desirability  we  have  two,  which  may  be  distinguished 
as  "regressive"  and  "progressive." 


APPENDIX   TO    CHAPTER   VII 

§  1  (TO  CH.  7,  §  1) 
Specimen  Definitions  of  Income 
Murray,  English  Dictionary  on  Historical  Principles,  1901. 

Income :  6.  spec\_ificattu~].  That  which  comes  in  as  the 
periodical  produce  of  one's  work,  business,  lands,  or  invest- 
ments (considered  in  reference  to  its  amount,  and  commonly 
expressed  in  terms  of  money);  annual  or  periodical  receipts 


346  NATURE    OF   CAPITAL   AND    INCOME 

accruing  to  a  person  or  corporation ;  revenue.  Formerly  also 
in  pi.  =  receipts,  emoluments,  profits ;  but  the  plural  is  now 
used  only  in  reference  to  more  than  one  person.  (The  prevail- 
ing sense.)  1601,  R.  Johnson,  Kingd.  &  Commun.  (1603)  196. 
Paying  the  expense  of  one  yere  with  the  income  of  another. 
1633,  Herbert,  Temple,  Ch.  Porch.  XXVII.  Never  exceed  thy 
income.  1646,  H.  Laurence,  Comm.  Angells.  152.  Hee  hath 
beene  at  a  great  deale  of  paines  and  cost ;  now  what  are  his 
in-comes  ?  1652,  C.  B.  Stapylton,  Herodian,  16.  He  scraped 
still  and  never  was  content,  But  studied  more  his  Incomes  to 
augment.  1697,  Dryden,  Virg.  Georg.  II,  285.  No  Fields  afford 
So  large  an  Income  to  the  Village  Lord.  1789,  Loiterer,  No. 
43,  10.  Having  lived,  what  is  called  up  to  his  income,  that  is, 
a  good  deal  above  it.  1802,  Med.  Jrnl  VIII,  229.  Income,  in 
its  usual  acceptation,  is  a  loose  and  vague  term ;  it  applies 
equally  to  gross  receipts  and  to  net  produce :  But  when  the 
Legislature  had  limited  it  to  be  synonimous  with  profits  and 
gains,  it  became  as  clear  and  precise  as  any  other  word.  1866, 
George  Eliot,  F.  Holt,  ii,  1, 76.  No,  I  shan't  attack  the  Church  — 
only  the  incomes  of  the  bishops,  perhaps,  to  make  them  eke 
out  the  incomes  of  the  poor  clergy. 

These  definitions  afford  no  means  of  deciding  on  net  income.  If  in- 
come is  simply  what  comes  in  and  outgo  simply  what  goes  out,  and  if  in 
any  year  as  much  passes  out  of  one's  hands  as  comes  in,  is  the  net  income 
zero  ? 

Dr.   N.  G.  Pierson,  Principles  of  Economics  Trans,  by  A.  A. 
Wotzel,  Vol.  I,  p.  76.      London  (Macmillan  &  Co.),  1902. 

By  social  income  we  mean  the  sum-total  of  economic  goods 
which  a  nation  has  at  its  disposal  in  a  given  period  of  time; 
the  net  result  of  the  productive  labour  of  the  nation  during  that 
time. 

Is  not  its  capital  "  at  its  disposal "  in  any  period  ?     Is  it  then  income  ? 

Roscher,  Principles  of  Political  Economy  (2d  vol.,  Eng.  trans., 
p.  5),  speaking  of  national  wealth,  says  that  gross  income  con- 
sists of,  — 

"  (a)    Of  the  raw  material  newly  obtained  in  the  country. 

"  (b)  Of  imports  from  foreign  countries,  including  that  which 
is  secured  by  piracy,  war  booty,  contributions,  etc. 


APPENDIX    TO    CHAPTKR    Vll  o47 

"  (c)  The  increase  of  values  which  industry  and  commerce 
add  to  the  first  two  classes  up  to  the  time  of  their 
final  consumption. 

"  (d)  Services  in  the  narrower  sense  and  the  produce  of 
capital  in  use. 

"  To  find  the  national  net  income  we  must  deduct  the  follow- 
ing items :  — 

"(a)    All  the  material  employed  in  production  which  yields 

no  immediate  satisfaction  to  any  personal  want. 
"  (6)    The  exports  which  pay  for  the  imports. 
"  (c)    The  wear  and  tear  of  productive  capital  and  capital  in 

use." 

The  method  thus  illustrated  is  the  method  which  takes  its 
starting  point  from  the  goods.  There  is  another  method  which 
takes  its  starting  point  from  the  persons  who  receive  them. 
By  this  method  the  national  income  is  to  be  calculated  as 
follows :  — 

"(a)  From  the  net  income  of  all  independent  private  busi- 
nesses, etc. 

"  (6)  From  the  net  income  of  the  state,  of  municipalities, 
corporations  and  institutions,  derived  from  their 
own  resources. 

"  (c)  Under  the  former  heads  must  be  taken  into  the  account 
such  parts  of  property  as  have  been  immediately 
consumed  and  enjoyed. 

"(cT)  Interest  on  debt  must  be  added  only  on  the  side  of 
the  creditor  and  deducted  from  the  income  of  the 
debtor." 

How  is  double  counting  to  be  avoided  if  "  raw  materials  produced" 
(a)  are  income  and  also  "the  produce  of  capital  in  use"  (d)?  "Increase 
of  values"  (c)  is  not  income  but  capital. 

Alfred  Marshall,  Principles  of  Economics,  Vol.  I,  pp.  149,  150. 

London  (Macmillan),  1898. 

"Another  convenient  term  is  the  usance  of  wealth.  It  means 
the  whole  income  of  benefits  of  every  kind  which  a  person 
derives  from  the  ownership  of  wealth,  whether  he  uses  it  as 
capital  or  not.  Thus  it  includes  the  benefits  which  he  gets 


348  NATURE    OF    CAPITAL   AND    INCOME 

from  the  use  of  his  own  piano,  equally  with  those  which  a 
piano  dealer  would  win  by  letting  out  a  piano  on  hire. 

"  This  income  is  most  easily  measured  when  it  takes  the  form 
of  a  payment  made  by  a  borrower  for  the  use  of  a  loan  for, 
say,  a  year ;  it  is  then  expressed  as  the  ratio  which  that  pay- 
ment bears  to  the  loan,  and  is  called  interest.  But  this  term 
is  also  used  more  broadly  to  represent  the  money  equivalent  to- 
the  whole  income  which  is  derived  from  capital. 

******* 

"Social  income  may  be  estimated  by  adding  together  the 
incomes  of  the  individuals  in  the  society  in  question,  whether 
it  be  a  nation  or  any  larger  or  smaller  group  of  persons. 
Everything  that  is  produced  in  the  course  of  a  year,  every  serv- 
ice rendered,  every  fresh  utility  brought  about  is  a  part  of  the 
national  income. 

"We  must  be  careful  not  to  count  the  same  thing  twice. 
If  we  have  counted  a  carpet  at  its  full  value,  we  have  already 
counted  the' values  of  the  yarn  and  the  labour  that  were  used 
in  making  it ;  and  these  must  not  be  counted  again.  But  if 
the  carpet  is  cleaned  by  domestic  servants  or  at  steam  scouring 
works,  the  value  of  the  labour  spent  in  cleaning  it  must  be 
counted  in  separately ;  for  otherwise  the  results  of  this  labour 
would  be  altogether  omitted  from  the  inventory  of  those  newly- 
produced  commodities  and  conveniences  which  constitute  the 
real  income  of  the  country." 

"Usance  of  wealth"  is  apparently  identical  with  income  as  explained 
in  this  book.  "Social  income,"  however,  seems  at  variance  with  the 
concept  of  "  usance  "  ;  for  it  includes  concrete  wealth. 

William   Smart,    TJie   Distribution   of  Income,  London  (]\Iac- 

millan),  1899,  p.  18. 

"In  any  case,  the  attempt  at  classification  seems  to  bring 
out  clearly  that  there  are,  conceivably,  two  ways  of  computing 
the  real  National  Income:  the  one  which  takes  it  as  the  sum 
of  consumption  goods  plus  any  additions  to  capital,  the  other 
which  takes  it  as  the  sum  of  the  services  which  contribute 
to  the  making  of  them  ;  and  that  these  two  are  alternatives. 
Either  alternative,  however,  may  be  used  when  different  pur- 
poses are  in  view ;  and  the  thesis  which  I  put  forward  is  that, 


APPENDIX   TO   CHAPTER   VII  349 

while  the  National  Income  must  be  conceived  of  as  the  total 
sum  of  consumption  goods,  as  these  and  these  alone  are  the 
means  of  satisfying  the  end  of  economic  action,  the  life  of  man, 
it  must  be  calculated  as  the  sum  of  the  contributory  services." 
Includes  concrete  goods  and  abstract  services. 

F.  W.  Taussig,  Wuyes  and  Capital  (Appleton  &  Co.,  New 
York),  1906,  p.  36. 

"  It  would  seem  best,  therefore,  to  lot  the  term  capital  stand 
simply  for  inchoate  wealth  :  for  all  the  possessions  that  do  not 
yet  serve  human  wants.  Tools  and  machines,  factories  and  ware- 
houses, raw  materials  and  half-finished  and  nearly  finished 
goods, — these  all  go  together  as  being  not  directly  conducive 
to  enjoyment;  while  all  forms  of  finished  commodities  —  food, 
houses,  clothes,  ornaments  —  belong  together  as  enjoyable 
wealth  and  as  income." 

Are  houses  income  ? 

Henry  Kogers  Seager,  Introduction  to  Economics  (Holt  &  Co., 
New  York),  1904,  pp.  1G3-1G4. 

"The  money  income  is  merely  the  convenient  medium  by 
means  of  which  the  real  income  of  the  community  is  divided 
among  those  entitled  to  share  it.  This  real  income  consists  of 
consumable  goods  for  those  Avho  spend  their  entire  money 
incomes,  and  partly  of  consumable  goods  and  partly  of  capital 
goods  for  those  who  save." 

As?  to  the  inclusion  of  "savings"  under  Income,  see  text  of  this  chapter 
and  the  fuller  treatment  in  Chapter  XIV. 

Charles  Jesse  Bullock,  Introduction  to  the  Study  of  Economics, 
rev.  ed.  Boston  (Silver,  Burdett  &  Co.),  1900,  p.  376. 

"In  this  way  the  social  income  for  any  month  or  year  may 
be  divided  into  four  constituent  parts :  — 

"1.  The  satisfactions  derived  from  durable  consumable  goods, 
the  product  of  past  industry,  that  still  remain  in  the  possession 
of  the  community  and  add  to  its  material  enjoyments. 

"2.  The  personal  services  at  the  disposal  of  the  society  dur- 
ing the  period  for  which  the  income  is  computed. 

"3.  The  material  goods  of  a  consumable  character  that  are 
the  product  of  the  current  industry  for  the  period  considered. 


350  NATURE    OF    CAPITAL    AND    INCOME 

"4.  The  producers'  goods,  or  capital,  created  by  the  current 
industry  of  the  period,  and  available  for  the  production  of 
economic  goods  during  the  following  periods." 

Is  double  counting  avoided  ;  e.g.  Are  material  goods  to  be  counted,  and 
then,  in  addition,  the  satisfactions  from  them  ? 

Frank  A.  Fetter,  The  Principles  of  Economics,  New  York  (The 
Century  Co. ),  1904,  pp.  40,  41. 

3.  "  Objective  income  consists  of  the  additional  sums  of  goods 
acquired  by  individuals  or  by  society  daring  the  income  period. 

******* 

4.  "  Income  in  the  logical  sense  must  be  a  net  addition,  but  the 
term  gross  income  is  not  ivithout  popular  and  practical  meaning. 
Gross  income  is  sometimes  spoken  of  in  the  sense  of  total 
receipts,  as  the  total  of  goods  secured;  net  income  is  the  re- 
mainder after  deducting  expenditures  and  after  replacing  the 
goods  employed  to  secure  the  income.     In  order  to  produce 
some  goods  technically,  men  make  use  of  other  goods.     While 
they  are  storing  up  a  supply  of  wood  or  coal  it  may  be  looked 
upon  as  the  income,  but  they  may  burn  it  to  help  grow  hot- 
house plants.      While  they  gather  flowers  with  one  hand,  they 
destroy  fuel  with  the  other.     Only  the  net  increase  in  value 
can  be  accounted  income  in  the  second  period.     The  goods 
that  come  into  a  man's  possession  in  any  period  are  of  many 
sorts :  to  get  some  he  has  destroyed  many  previously  existing 
goods;  while  to  get  others  he  has  not  needed  to  use  up  the 
accumulations  of  the  past  or  to  mortgage  the  future.     The  one 
kind  is  gross,  the  other  net  income. 

5.  "  An  income  of  consumption  goods  is  a  part  of  wealth,  but 
not   the   ivhole  of  it.     The   consumption    goods,   the    'present 
goods'   at   the   moment   available,  are  the  essential  part  of 
wealth  for  the  moment's  enjoyment.     The  only  essential  and 
immediate  conditions  of  a  series  of  gratifications  is  a  regular 
series  of  consumption  goods.     But  many  things  existing  which 
could  be  used  to  secure  a  gratification  are  not  in  fact  treated 
as  consumption  goods.      A  crop  of  corn  is  not  all  income.      In 
a  time  of  famine  it  could  be  used,  but  seed-corn  was  saved  from 
last  year,  and  some  must  be  kept  for  next  year.     This  is  a 


APPENDIX    TO    CHAPTKH    VII  351 

part  of  wealth,  but  not  of   'present  goods'    as  we  understand 
the  term." 

"Goods"  are  not  income.    Increase  of  value  is  not  income.    See  text. 

Kleinwachter,  Das  Einkommen  und  seine  Verteiluny,  Leipzig, 
1896,  pp.  11,  12. 

So  bestimmt  beispielweise  das  Einkommensteuergesetz  fur. 
Hamburg  vom  26.  Marz,  1880,  iin  Sec.  4:  — 

"Die  Einkommensteuer  ist  von  dem  reinen  Einkommen  oder 
Erwerb  zu  entrichten,  d.  h.  alien  in  Geld  oder  Geldeswert 
(etwaige  selbstverwohnte  Miete,  den  Wert  etwaige  freier 
Wohnnng,  Naturallieferungen  u.  s.  f.  hinzugerechnet)  beste- 
henden  Einnahmen  des  Steuerpfliehtigen,  ohne  Ausnahme, 
gleichgiltig  aus  welcher  Quelle  sie  geflossen.  .  .  . " l 

Ahnlich  sagt  das  sachsische  Einkommensteuergesetz  vom  2. 
Juli,  1878,  im  §15:- 

"Als  Einkommen  gilt  die  Summe  aller  .  .  .  Einnahmen  mit 
Einschluss  des  Mietwertes  der  Wohnung  im  eigenen  Hause, 
sowie  des  Wertes  der  zum  Haushalt  verbrauchten  Erzeugnisse 
der  eigenen  Wirtschaft.  .  .  ." 

Und  fast  mit  denselben  Worten,  nur  etwas  minutioser  und 
genauer,  sagt  der  osterreiehische  Entwurf  eines  Gesetzes, 
betreffend  die  direkten  Personalsteuren  vom  Jahre  1892,  im 
§  195 :  - 

"Als  Einkommen  gilt  die  Summe  aller  in  Geld  oder  Geldes- 
wert bestehenden  Einnahmen  der  einzelnen  Steuerpfliehtigen 
in  it  Einschluss  des  Mietwertes  der  Wohnung  im  eigenen  Hause 
oder  sonstiger  freier  Wohnung,  sowie  des  Wertes  der  zum 
Haushalte  verbrauchten  Erzeugnisse  der  eigenen  AVirtschaft 
und  des  eigenen  Gewerbebetriebes,  sowie  sonstiger  dem 
Steuerpfliehtigen  allenfalls  zukommender  Xaturalemgange." 

Bemerkenswert  ist,  dass  keine  dieser  Gesetzesstellen  die 
einzelnen  Arten  oder  Zweige  oder  Bestandteile  des  Einkom- 
mens,  die  der  Steuer  unterworfen  sein  sollen,  taxativ  aufzahlt, 
sondern  dass  die  in  Rede  stehenden  Gesetze  das  "Einkommen" 
ganz  allgemein  zu  definieren  bestrebt  sind.  Und  der  Tenor  ist 
jedesmal :  "  Unter  Einkommen  versteht  man  allc  in  Geld  oder 


352  NATURE    OF    CAPITAL    AND    INCOME 

Geldeswert  bestehenden  Einnahmen,gleichgiltig  aus  welcher  Quelle 
sie  geflossen."  Da  nun  in  unserer  heutigen  auf  cler  Grundlage 
des  Privateigentums  und  der  Individual wirtschaft  aufgebauten 
Volkswirtschaft 

1.  alle  erdenklichen  Sachgiiter, 

2.  alle  erdenklichen  Nutzungen  dieser  Sachgtiter  und 

3.  alle  erdenklichen  personlichen  Dienstleistungen  um  Geld 
verkauft  und  gekauft  werden  konnen  und  demgemass  "  Geldes- 
wert haben,"  so  ergiebt  sich,  dassder  Gesetzgeber  alle  inateriel- 
len  und    imniateriellen    Gtiter,    die    in   die    Wirtschaft    des 
Einzelnen   treten,    unter   den    Begriff   des    Einkommens    sub- 
sumiert  wissen  will.  .  .   .  Das  heisst  also  mit  anderen  Worten: 
der  Gesetzgeber  definiert  den  Einkommensbegriff  in  der  nam- 
lichen  Weise,  wie  es  oben  definiert  wurde,  und  zwar  so,  dass 
unter   "Einkommen"   alle   Guter  verstanden   werden   sollen, 
welche   entweder   in   die   eigene  Wirtschaft  von  aussen  her- 
einkommen,  oder  welche  innerhalb  der  eigenen  Wirtschaft  neu 
entstehen,  und  zwar  gleichgiltig  ob  diese  Guter  materielle  (oder 
Sach-)    Gtiter,  oder  ob  sie  immaterielle  Guter  (d.  i.  Nutzungen 
von  Sachgiitern  oder  personliche  Dienstleistungen)  sind. 

To  include  in  income  all  newly  acquired  or  newly  produced  goods  is 
clearly  to  include  too  much.  To  restrict  income  to  money  receipts  is,  as 
shown  in  the  text,  to  err  both  in  inclusion  and  exclusion.  To  require  that 
the  income  shall  be  "rein"  or  "net"  without  denning  the  deduction 
required  to  make  it  so  is  to  leave  the  definition  incomplete. 

Kleinwachter,  op.  cit.,  pp.  22-23. 

An  dieser  Stelle  genligt  die  Bemerkung,  dass  die  HER- 
MANN-ScuMOLLERSCHE  Definition  oder  Auffassung  des 
(Einzel-)  Einkommens  bis  auf  den  heutigen  Tag  so  ziemlich 
(die  abweichenden  Meinungen  sollen  weiter  unten  erwahnt 
werden)  die  herrschende  geblieben  ist.  HERMANN  ("  Staats- 
wirtschaftliche  Untersuchungen."  2.  Aufl.,  Miinchen,  1870, 
S.  582  u.  583)  definiert  das  (Einzel-)  Einkommen  wie  folgt: 

"So  wenig  jede  Ausgabe  Verbrauch  ist,  so  wenig  ist  jede 
Einnahme  Einkommen.  Dieses  ist  vielmehr  die  Summe  der 
wirtschaftlichen  oder  Tauschgtiter,  welche  in  einer  gewissen 
Zeit  zu  dem  ungeschmalert  fortbestehenden  Stammgut  einer 
Person  neu  hiuzutreten,  die  sie  daher  beliebig  verwenden  kann. 


APPKNDIX   TO   CHAPTER   VII  353 

Dass  es  ebensowohl  korperlicher  als  unkorperlicher  Natur  sein 
konne,  1st  klar." 

Und  im  Anschlusse  an  diese  HERMANNSCHE  Definition  des 
Einkommeiis  sagt  SCHMOLLER  ("Die  Lehre  vom  Einkommen 
u.  s.  w."  in  der  "Zeitschr.  f.  d.  ges.  Staatsw. "  Jahrg.  18G3, 
Bd.  19,  S.  1  ff.  speciell  S.  19):  - 

"  Einkommen  ist  .  .  .  also  die  Sumrae  von  wirtschaftlichen. 
Giitern,  die  ein  Subjekt  in  einer  gewissen  Zeit  zur  Befriedigung 
seiner  Bediirfnisse  ohne  Schmalerung  seines  Vermogens  ver- 
wenden  kann.  Fur  Jeden  sind  die  Friichte  seiner  Arbeit  und 
seines  Vermogens  sein  urspriingliches  Einkommen;  ein  ab- 
geleitetes  hat  nur  der,  welcher  solche  Friichte  nicht  hat ;  d.  h. 
nur  er  lebt  vom  Einkommen  anderer.  .  .  .  Zum  Einkommen 
gehoren  stets  auch  samtliche  unmittelbar,  d.  h.  ohne  Tausch, 
yerbrauchten  oder  genossenen  Friichte  der  Arbeit  und  des 
Vermogens." 

The  foregoing  definitions  express  in  a  general  way  what  we  have  called 
"  earnings  "  as  distinct  from  "  income."  They  err  however  by  fixing  on 
concrete  commodities  in  place  of  their  services  and  in  some  other  respects. 
See  text. 

In  erschopfender  Weise  hat  ADOLF  WAGNER  die  aus  der 
bisher  geschilderten  Auffassung  entspringenden  Einkommens- 
/defini tionen  in  seiner  bekannten  "  Grundlegung  "  (1.  Aufl.,  S.  96 
u.  97  )  zusammengefasst,  wenn  er  das  Einzelneinkommen  defin- 
iert  wie  folgt:  — 

"Im  Einkommen  (einzeln  in  den  Einkiinften)  werden  die 
Einnahmen  oder  Ertrage  in  Beziehung  mit  der  Person,  welche 
•sie  empfangt,  daher  rait  dem  Wirtschaftssubjekte  gebracht. 
Das  Einkommen  einer  Person  umfasst  zweierlei:  — 

"1.  Diejenige  Summe  wirtschaftlicher  Gu'ter,  welcher  der- 
.selben  in  gewissen  Perioden  .  .  .  regelmassig  und  daher  mit 
der  Fahigkeit  der  regelmiissigen  Wiederholung  als  Reinertrftge 
einer  festen  Erwerbsquelle  neu  als  Vermogen  hiuzuwachsen. 
Dieser  Teil  des  Einkonimens  einer  Person  riihrt  daher  aus  der 
"Wirtschaftsfiirung  iiberhaupt  und  aus  einzelnen  wirtschaft- 
lichen  Thatigkeiten  (Arbeit,  Unternehmung)  oder  aus  Eigen- 
tums-  oder  Forderungsrechten  inbesondere  (Sklaveneigentum, 
Grundeigentum,  Kapitaleigentum,  Forderungen  aus  Kreditge- 


354  NATURE    OF   CAPITAL   AND    INCOME 

schaften),  endlich  aus  regelmassigen  unentgeltlichen  Ein- 
nahraen  (Almosen,  Geschenk)  her. 

"  2.  Die  Gentlsse  (Nutzungen)  oder  selbst  nur  die  Genuss- 
moglichkeiten,  welche  das  Nutzvermogen  einer  Person  nach 
Abrechnung  der  dabei  stattfindenden  Abnutzung  und  Verkehrs- 
wertverminderung  periodisch  fortdauernd  gestattet. 

"  Das  Einkommen  einer  Person  bildet  zunachst  den  Gtiterf  ond 
zur  Befriediguiig  ihrer  Bedtirfnisse.  Seine  Erwerbung  ist  das 
Mittel  zu  letzterem  Zwecke.  Es  kann  in  derselben  Periode, 
in  der  es  erlangt  wurde,  vollstandig  verzehrt  werden,  ohne  dass 
dadurch  das  friihere  Vermogen  geschmalert  wird.  Die  Tausch- 
werthohe  des  Einkommens  einer  Person  entscheidet  iiber  das 
Mass  der  letzterer  moglichen  dauernden  Bedurfnisbefriedigun- 
gen,  ist  daher  volkswirtschaftlich  von  grosster  Bedeutung." 

The  errors  in  Wagner's  definition  are  the  restriction  that  income  must 
be  "regular"  and  the  inclusion  of  concrete  commodities  and  abstract 
services,  side  by  side. 

Klein wachter,  op.  cit.,  p.  24. 

.  .  .  man  heute  unter  dem  Einkommen  einer  Person  ver- 
steht :  — 

alle  Guter,  welche  in  die  Wirtschaft  oder  in  das  Vermogen 
einer  Person  treten,  und  zwar  :  — 

1.  gleichgiltig,   ob  diese    Gtiter   von  aussen   in   die   eigene 
Wirtschaft  hereinkommen,  oder  ob  sie  innerhalb  der  eigenen 
Wirtschaft  neu  entstanden  sind,  und 

2.  gleichgiltig,  ob  diese  Giiter  materieller  oder  unmateriel- 
ler  Natur  sind. 

Allerdings  mussen  in  diese  Definition  zwei  weitere  Momente 
aufgenommen  werden,  wenn  dieselbe  die  heutige  communis 
opinio  der  Wissenschaft  widerspiegeln  soil,  zwei  Momente,  die 
ich  in  der  "Einleitung"  mit  Vorbedacht  unberiicksichtigt 
gelassen  habe,  weil  sie  flir  den  mir  dort  vorschwebenden  Zweck 
bedeutungslos  waren,  namlich  :  — 

1.  dass  die  in  Rede   stehenden  Giiter  mit  einer  gewissen 
Regelmassigkeit  in  die  Wirtschaft  oder  in  das  Vermogen  der 
betreffenden  Person  treten  miisseri,  wenn  sie  als  "Einkommen" 
gelten  sollen,  und 

2.  dass  diese  Giiter  nur  dann  als  "Einkommen"  aufcrefasst 


AI'I'KNMX   TO   CHAPTER   VII  355 

werden  konnen,  wenn  sie  neu  in  die  Wirtschaft  oder  in  das 
Vermogen  der  betreffenden  Person  treten,  d.  h.  also  wenn  sie 
zu  dein  bisherigen  Vermogen  der  betreffenden  Person  hinzu- 
treten,  oder  mit  anderen  Worten:  es  Hegt  ningekelirt  kein 
"Einkommen"  vor,  wenn  Giiter  in  die  eigene  Wirtschaft  her- 
einfliessen,  welche  Teile  des  Stammvermogens  dieser  Wirtschaft 
sind,  also  beispielweise,  wenn  ausstehende  Forderungen  zu- 
ruckgezahlt  oder  ausgeliehene  Vermogeuobjekte  zuriickgestellt 
werden. 

According  to  Kleinwachter  the  effort  to  reach  a  self-consistent  concept 
of  income  had  led  to  the  inclusion  of  every  element  flowing  into  one's 
possession  whether  by  exchange  from  without  or  by  production  from 
within  his  own  establishment,  and  whether  these  elements  are  material  or 
immaterial,  so  long  as  we  exclude  such  elements  as  "  irregular  "  receipts 
and  the  return  of  old  debts.  The  uselessness  of  such  a  concept  Klein- 
wachter himself  points  out. 

Robert  Meyer,  Handworterbuch  der  Staats-  Wissenschaften,  Bd. 
Ill,  Art.  Einkommen  "Begriff,"  p.  348. 

Die  englische  liberals  National  okonomie  war  von  dieser 
Grundlage  aus  zu  einseitigen  Resultaten  gelangt,  indem  sie  das 
Einkommen  ganz  in  der  Art  verstand,  wie  die  Buchhaltung 
einer  kaufrnannischen  oder  industriellen  Unternehmung  den 
Reingewinn  ermittelt. 

******* 

Die  deutsche  Litteratur  hat  diese  Einseitigkeit  vermieden, 
und  die  bis  auf  die  Gegenwart  herrschend  gebliebene  Her- 
mannsche,  von  Schmoller  erganzte  und  vielleicht  liber  Gebiihr 
viel  bewunderte  Lehre  versteht  unter  Einkommen  alle  Tausch- 
giiter,  die  nach  vollstandiger  Herstellung  alles  Stammver- 
mogens innerhalb  des  Jahres  neu  erzeugt  und  dargeboten 
werden  und  zur  Befriedigung  der  Bediirfnisse  der  Xation 
dienen  mogen  (Hermann),  oder  die  Sum  me  der  wirtschaftlichen 
Guter,  die  ein  Subjekt  in  einer  gewissen  Zeit  zur  Befriedigung 
seiner  Bediirfnisse  ohne  Schmiilerung  seines  Vermogens  wer- 
wenden  kann  (Schmoller) . 

******* 

In  neuerer  Zeit  ist  ein  friiher  als  selbstverstandlich  vor- 
ausgesetztes  Merkinal  auch  begrifflich  in  den  Yordergrund 


356  NATURE   OF   CAPITAL   AND    INCOME 

gestellt  worden:  die  Wiederkehr,  die  regelmassige  Wieder- 
kehr  oder  die  Fahigkeit  der  Wiederkehr  der  das  Einkommen 
bildenden  Einnahmen. 

******* 
Formliche  Definitionen  des  Einkommens  werden  haufig 
verruieden,  doch  sagt  die  sachsische  Einkommen steuer  vom  2. 
Juli,  1878,  §  25:  Als  Einkommen  gilt  die  Summe  aller  in 
Geld  und  Geldeswert  bestehenden  Einnahmen  abzuglich  der 
auf  Erlangung,  Sicherung  und  Erhaltung  dieser  Einnahmen 
verwandten  Ausgaben  sowie  etwaiger  Schuldzinsen,  auch  in- 
sofern  diese  nicht  zu  den  eben  bezeichneten  Ausgaben  gehoreii, 
Ausserordentliche  Einnahmen  durch  Erbschaft  und  ahnliche 
Erwerbungen  gelten  jedoch  nicht  als  steuerpfiichtiges  Einkom- 
men, sondern  als  Vermehrung  des  Stammvermogens.  Ganz 
ahnlich  das  osterreichische  G.  v.  25.  Oktober,  1896,  welches 
jedoch  den  zweiten  Absatz  anders  gefasst  hat:  — 

"Ausserordentliche  Einnahmen  aus  Erbschaften,  Lebens- 
kapitalsversicherungen,  Schenkungen  und  ahnlichen  unentgelt- 
lichen  Zuwendungen  gelten  nicht  als  steuerpflichtiges  Ein- 
kommen." 

These  formulations  virtually  repeat  the  definitions  given  above. 

Franz  Guth,  Die  Lehre  vom  EinJcommen  in  dessen  Gesammt- 
zweigen,  Leipzig,  1878,  p.  62. 

Einkommen  ist  jede  aus  einer  Quelle,  also  mit  einer-gewissen 
Kegelmassigkeit  widerkehrende  Vermehrung  des  Vermogens. 
Der  Bezieher  Kann  es  geniessen,  verzehren,  oder  auf  irgend 
einer  Art  vernichten,  ohne  seinen  Fonds  zu  schwachen.  Lot- 
teriegewinne,  precare  Almosen  und  Geschenke  sind  daher  kein 
Einkommen,  wohl  aber  sind  es  Almosen  und  Geschenke,  die 
sich  auf  gewisse  Titel  grilnden. 

This  view  is  discussed  in  the  text. 


APPENDIX  TO  CHAPTER  XII  357 

APPENDIX   TO    CHAPTER   XI 

§  1  (TO  CH.  XI,  §  2) 
Dimensions  of  Income-capital  Ratios 

If  we  indicate  time  by  t  and  distinguish  the  quantity  and 
value  of  services  by  the  letters  q  and  v,  and  the  quantity  and 
value  of  capital  by  Q  and  V,  the  four  ratios  mentioned  assume 
the  form  :  — 

Physical  productivity,  _!L,  e.g.  bushels  per  acre  per  year. 
(^t 

Value  productivity,        ~,  e.g.  dollars  per  acre  per  year. 
Qji 

Physical  return,  -3-,  e.g.  bushels     per   dollar's   worth  of 

capital  per  year. 

Value  return,  —  ,  e.g.  dollars  per  dollar  (  i.e.  per  cent) 

per  year. 

APPENDIX   TO    CHAPTER   XII 
§  1  (TO  CH.  XII,  §  2) 

Mathematical  Relations  between  Rates,   Annually,  Semi-annually,  etc., 
when  conceived  in  the  Sense  of  the  Price  of  Capital 

If  i'  represents  the  rate  of  interest  per  annum  when  the 
income  is  payable  semi-annually  (such  as  4  %  in  the  example 
in  the  text)  and  i  the  rate  which  would  be  its  equivalent  when 
the  income  is  payable  annually  (such  as  4.04  %  in  the  example), 
the  relation  between  i'  and  i  is,  — 


To  show  this  we  observe  that  under  our  hypothesis  as  to  i 
and  i',  a  capital  of  $1  will  buy  a  perpetual  income  of  either  i 

i' 
each  year,  or  -  each  six  months.     Let  us  suppose,  as  in  the 

LI 

preceding  example,  in  six  months  the  holder  of  the   latter 
annuity,  after  receiving  his  first  installment  of  income,  -^,  sells 


358  NATURE    OF   CAPITAL   AND    INCOME 

out  for  $1,  which  he  may  evidently  do  if  the  rate  of  interest 
remains  unchanged.  With  his  total  receipts,  1  -f  -,  he  buys  a 
new  annuity  of  the  same  type.  This  will  evidently  yield  him 

1 1  -f  M  i'  per  annum,  payable  in  semi-annual  installments  of 
v  / 


half  that   amount,  or  -^ — ^-^ —  .     At  the  end  of  another  six 

Z/ 

months,  then,  he  receives  this  last-named  sum,  and,  selling  his 
newly  bought  annuity  for  its  original  value  of  1  -f  -,  he  has  in 


hand  a  total  sum  of  1  +--  -f--^ — - — ^- —     Of  this  sum  he    rein- 
vests $  1  and  retains  as  income  the  remainder,  or  -  +-  

This  sum  may  evidently  be  obtained  year  after  year  simply 
by  repeating  the  above  process.  It  constitutes  a  perpetual 
annuity,  payable  annually,  and  its  value  simplified  from  the 

above  formula  is  evidently  i'  +  — . 

Since  this  is  the  annual  income,  payable  annually,  which  $1 
of  capital  will  buy,  it  is  by  definition,  the  magnitude  we  called  i; 

i'2 

that  is,  i  =  i'  +  -  . 
4 

We  may  in  like  manner  proceed  to  quarterly  payments,  in 
which  case  we  shall  find,  by  analogous  reasoning,  denoting  by 
i"  the  rate  of  interest  per  annum  payable  quarterly,  that 

i=i"  +  Si"S-\  V<Z     *'"" 
8    + 16     256' 

§  2  (TO  CH.  XII,  §  4) 

Mathematical  Relations  between  Rates  reckoned  Annually,  Semi-annually, 
etc.,  when  Rates  are  conceived  as  "  Premiums."  Diagrammatic  Rep- 
resentation. Economic  Interpretation  of  e. 

In  general  let  i'  be  the  rate  of  interest  per  annum  reckoned 
semi-annually.  Then  the  "  amount "  of  $1  in  six  months  is 


APPENDIX    TO   CHAPTER    XII  359 

SI 

1  -|-  -  ,  and  this  sum  in  another  six  months  will  "  amount  "  by 

-  /  ft  \  2 

compound  interest  to  (  1  +   ..  \  ,  which  must  be  equal  to  1  -f  f, 
\         2y 

the  "  amount  "  of  $1  in  one  year  at  the  equivalent  rate  of  inter- 
est, /,  reckoned  annually;  i.e. 


or,  expanding  and  reducing,  — 


which  is  the  same  result  obtained  before  when  the  rate  of 
interest  was  regarded  as  the  price  of  capital. 

Similarly,  for  the  interest  rate  i",  reckoned  quarterly,  we 

/  ,j"\4 

may  prove  1  +  i  =  f  1  -\  --  )  ,    and   for   the    interest    rate  i(n\ 

/         ?'(n)\n 
reckoned  n  times  a  year,  1  +  i  —1  1  -\  ---  )• 

\          n  J 
In  other  words, 


n  j       |_\          n 

As  n  increases  indefinitely,  the  last  expression  approaches  a 
limit.  The  limit  of  i(n>  is  the  "  rate  of  interest  per  annum  com- 
puted continuously,"  called  8.  The  limit  of  the  square  bracket 
is  the  base  of  the  Napierian  system  of  logarithms  called  e;  for 

f        IV 
by  the  definition  of  e  usually  given,  it  is  the  limit  of  ( 1  +  -  J, 

V        */ 
when   k  is   any   number    increasing    indefinitely.     Evidently 

—  is  such  a  number,  for  n,  by  hypothesis,  is  to  be  increased 

indefinitely,  and  i(n>  evidently  decreases.  Hence  at  the  limit 
the  last  formula  becomes, 

Or,  substituting  for  e  its  numerical  value, 
1  +  i  =  (2.7182818)5. 

Another  proof  of  this  formula  could  be  given  for  the  case 
where  the  rate  of  interest  is  conceived  as  the  price  of  capital, 


360  NATURE   OF   CAPITAL   AND    INCOME 

by  following  to  the  limit  the  method  of  this  Appendix,  §  1 
above. 

The  number  e,  or  2.7182818,  plays  almost  as  important  a  role 
in  mathematics  as  the  number  3.141592,  called  TT,  which 
expresses  the  ratio  of  the  circumference  of  a  circle  to  its  diam- 
eter, but  the  meaning  of  e  is  less  familiar  to  most  students. 
Various  definitions  and  interpretations  may  be  given.  To  the 
economist,  the  most  interesting  is  the  following:  e  is  the 
"amount"  of  $1  put  at  compound  interest  during  the  "pur- 
chase period,"  the  latter  being  derived  on  the  assumption  that 
the  rate  of  interest  is  payable  continuously. 

This  proposition  is  implicitly  contained  in  the  demonstra- 
tion of  the  equation  1  +  i  =  e5,  as  given  above.  The  following 
is  a  more  explicit  statement,  with  actual  illustrative  figures :  — 

If  we   consider   the   rate  of  interest  4%,  or  -    -   payable 

100 

annually,   the   purchase   period  is  25  years,  or  ,  and  the 

amount  of  $1  put  at  4%  interest  for  these  25  years  will  be 

(H-.04)25. 

If  next  we  take  4%  payable  semi-annually,  the 
amount  of  $1  during  the  purchase  period  of  25     f*       .04V0 
years  will  be  \         2  j 

Similarly,  the  amount  of  $1  put  at  interest  at  A,    .    .04V00 
4%  payable  quarterly  is  \          4  J 

And  if  the  interest  is  reckoned  as  payable  n    /..       -^ 
times  a  year,  the  amount  is  \         n 

At  the  limit,  we  have  the  amount  of  $1  at  interest  at  4% 
for  25  years  when  the  rate  of  interest  is  payable  continuously. 
The  limit  of  the  above  expression,  when  n  is  made  indefi- 
nitely great,  is  the  definition  of  e. 

The  distinction  between  the  different  rates  of  interest  may 
be  shown  by  a  diagram.  In  Figure  33,  let  the  curve  B'AB  rep- 
resent a  "discount  curve,"  any  two  ordinates  of  which  represent 
exchangeable  goods  situated  at  two  corresponding  points  of 
time,  as  a  and  b,  that  is,  the  sum  a  A  of  "  present "  goods  will  buy 
the  sum  bB  of  goods  which  lie  in  the  future  a  time  interval  ab, 
beyond  the  "present."  If  we  take  these  two  points,  a  and  b,  a 
year  apart,  the  rate  of  interest  as  reckoned  annually  is  the 


APPENDIX   TO    CHAPTER   XII 


361 


"slope"  of   the  secant   AB   in   relation   to   the   ordinate   a  A 
(—-—-:-  aA\     Similarly,  the  slope  of  the  secant  AC  drawn 

through  points  corresponding  to  times  a  half  year  apart,  taken 
in  relation  to  aA,  is  the  rate  of  interest  reckoned  seini-annually, 


and  so  on.  At  the  limit,  the  slope  of  the  tangent  AT  (in  re- 
lation to  aA)  represents  the  rate  of  interest  reckoned  continu- 
ously. 

Similarly,  the  regressive  secant,  AB',  represents  the  rate  of 
discount,  reckoned  annually  (if  ab'  represents  a  year  interval), 


362  NATURE    OF   CAPITAL   AND    INCOME 

AC?,  the  rate  reckoned  semi-annually,  and  so  on  until  the  tan- 
gent AT',  or  AT,  is  again  reached,  when  the  distinction  between 
interest  and  discount  disappears.  It  is  easy  to  prove  (by  simi- 
lar triangles)  that  the  reciprocal  of  the  rate  of  interest  continu- 
ously reckoned,  in  other  words  the  "year's  purchase,"  is 
represented  by  aS  the  subtangent. 

§  3  (TO  CH.  XII,  §  6) 

A  Premium  Rate  of  4%  one  Year  and  3%  Each  Year  after  means  a  Price 
Rate  of  3.03%  the  First  Year. 

We  have  given  4%  as  the  rate  of  interest  (as  premium)  in 
the  first  year,  and  3%  as  the  rate  for  each  year  thereafter. 

Let  us  suppose  that  $  100  to-day  is  invested  for  $  104  next 
year,  and  that  at  the  end  of  the  year,  of  this  $  104,  $  100  is  re- 
invested. Since  thereafter  the  rate  of  interest  is  always  3% 
in  the  premium  sense,  it  must  be,  by  proof  in  the  text,  also  3% 
in  the  price  sense.  Consequently,  the  $  100  reinvested  next 
year  may  be  used  to  buy  $  3  a  year  forever.  The  result  is  that 
for  the  $100  to-day  the  return  is  $4  next  year  and  $3  each 
year  thereafter.  This  series  of  payments  is  the  same  as  $3  a 
year  forever,  together  with  one  extra  dollar  at  the  end  of  the 
first  year.  This  extra  dollar  has  a  present  worth  (since  the 
interest  premium  between  this  year  and  next  year  is  4%)  of 
j^,  or  .96T2^.  If  we  deduct  this  present  value  of  the  extra 
dollar  from  the  $100  (which  is  the  present  value  of  the  entire 
series  of  $4,  $3,  $3,  $  3,  etc.,  ad  inf.),  we  have  the  present 
value  of  the  series  without  the  extra  dollar,  i.e.  of  $3  a  year 
forever.  The  remainder  is  $99.03^.  Since,  then,  this 
$99.03{-|  will  buy  $3  a  year  forever,  the  rate  of  interest  in  the 
price  sense  is  $3  -H  $99.0311,  Or  3.03%  approximately.  This 
is  the  rate  at  the  outset.  After  the  first  year  it  will  evidently 
always  be  3%. 

§  4  (TO  CH.   XII,  §  6) 

A  Price  Rate  of  4  %  this  Year  and  3  %  Each  Year  after  means  a  Premium 
Rate  of  37|  %  the  First  Year. 

We  have  given  4  °/0  as  the  rate  (in  the  price  sense)  for  the 
first  year,  and  3%  as  the  rate  (in  the  same  sense)  for  each  year 
after. 


APPENDIX  TO  CHAPTKR  XII  363 

$100  will  to-day  buy  the  right  to  $4  a  year  forever,  and  a 
year  hence  this  right  to  $4  annually  may  be  sold  on  a  3% 
basis.  It  will  therefore  fetch  $133.33.  The  investor  will 
consequently  receive  in  all,  at  the  end  of  this  first  year,  a  total 
of  $4-f  $133|,  or  $137^.  Hence  the  rate  of  interest  in  the 
sense  of  a  premium  will  be  for  that  year  37,^%.  In  succeed- 
ing years  the  rate  of  interest,  considered  either  as  a  premium  or 
a  price,  will  evidently  be  3%. 

§  5  (TO  Cu.  XII,  §  6) 

Mathematical  Relations  between  the  Rates  of  Interest  as  a  Premium  and 

as  a  Price 

In  general,  if  we  let  e\  represent  the  rate  of  interest  in  the 
premium  sense  for  this  year,  i2  for  next  year,  is  for  the  third 
year,  and  so  on,  whereas  ji,j2,  and  js,  etc.,  represent  the 
rates  of  interest  in  the  price  sense  for  the  same  successive 
years,  the  following  relations  between  the  i's  and  fs  may  be 
proved: — 

111 

_.  _j .  I j_  cLCl  lilt    — *: 

1    -  + -1 + - L _  +  ...  ad  inf. 


•       •   adinf.= 


— ^-  +  ,„   .   . .    7— 77  + /.   .    .^-<   .   .X/H    .   .,+...  ad  inf. 


•      -ad  inf.  = 


— r  +  „   ,   ..^    .    .x  +  ,.   .    .x/_    .    .  w_    ,    ..  +  ...  ad  inf. 


etc. 

These  equations  may  be  said  to  determine  _/„  as  a  peculiar 
sort  of  mean  of  the  magnitudes  i1}  t'2,  i:i,  ...  ad  inf.,  andj.,  as  a 
similar  mean  of  ?'2,  %,  z'4,  ...  ad  inf.,  etc.  Their  proof, 
which  is  simple,  is  left  to  those  readers  who  are  interested  in 
mathematics. 

The  preceding  equations  express  the  values  of  the  fs   in 


364  NATURE    OF   CAPITAL   AND    INCOME 

terms  of  i's.    The  following  equations  give  the  i's  in  terms  of 
the  fs  :  — 


h 

^—     '  — 


,'   _  ,' 

h—Js 


etc. 

Thus  if,  as  in  our  example,  ^  =  .04  and  j2  —  .03, 

m      .04  -.03       „„. 
i1  =  .04  +  -  __=.3/£. 

.U<_> 

The  proof  of  these  formulae  is  also  left  to  the  mathematical 
reader.  He  will  observe  that  the  two  sets  of  equations  may  be 
proved  independently  or  either  set  may  be  proved  and  the 
other  set  derived  from  it.  To  show  that  either  set  may  be  de- 
rived from  the  other,  it  will  be  found  useful  to  substitute  for 
the  left-hand  members  of  the  first  set  their  simpler  values  as 

derived  by  algebra.     These  are,  -,  -,  -,  etc.     An  easy  proof  of 

Ji  J'2  Ja 
this  is  found  by  actually  dividing  1  by  j1}  etc. 

From  the  formulae  it  is  clear  that  if  i\=  i2=  «'3=,  etc.,  then 
j1=ja=js=}  etc.,  and  that  then  all  the  i's  =  the  fs.  The 
converse  is  also  evident. 

§  6   (TO  CH.  XII,  §  7) 
Mathematical  Relations  between  the  Rates  of  Interest  and  Discount 

Let  V,  due  one  year  hence,  be  the  equivalent  of  V  available 
in  the  present.  Then  the  rates  of  interest  and  discount  are 
expressed  respectively  by  the  formulae  :  — 


-. 

v 

Whence,  by  multiplying  the  two  equations  together  we 
derive  (1  +  i)  (1  —  d)  =  l,  which  reduces  to  d  =  i—id.  That 
is,  the  number  representing  the  rate  of  discount  equals  the 
number  representing  the  equivalent  rate  of  interest  less  a 


APPENDIX    TO    CHAPTER    XII  365 

small  correction,  equal  to  the  product  of  the  rates  of  interest 
and  discount. 

The  relation  between  the  rates  of  discount  and  interest 
when  semi-annually  reckoned  is  analogous  to  the  relation  which 
we  found  between  those  annually  reckoned.  We  then  have 

V  d  ' 

the  equations,  —  =  1  —  — 

V  i' 

and  -=1- 


whence 

By  multiplication  and  reduction, 


We    may   apply   similar     reasoning   to  quarterly-reckoned 
interest  and  discount  rates. 

It  follows  that     fl  +  ^'Wl-— ^)  =  1, 
V       4  /  V        4  j 

or  d"=i"-1-^-. 

4 

The  same  reasoning  may  obviously  be  applied  to  reckonings 
71  times  a  year.     We  then  find, 


n 
It  is  evident  that  if  n,  the  number  of  parts  into  which  the 

year  is  divided,  be  sufficiently  increased,  the  term  —     —  be- 

n 

comes  infinitely  small,  so  that,  at  the  limit,  the  rate  of  interest 
and  the  rate  of  discount  become  equal.  This  rate  for  continu- 
ous reckoning,  being  the  same  as  the  rate  of  interest  for  con- 
tinuous reckoning,  is  also  called  S. 

Unlike  the  rate  of  interest,  the  rate  of  discount  is  always 
considered  as  associated  with  the  exchange  of  present  against 
future  goods,  and  not  with  the  exchange  between  capital  and 
income,  i.e.  is  taken,  not  in  the  "price"  sense,  but  in  the  "pre- 
mium" sense  (the  premium  being,  in  this  case,  negative).  We 
may,  however,  to  complete  our  scheme  of  concepts,  construct 
for  ourselves  a  "rate  of  discount"  in  the  sense  of  the  price  of 
capital  in  income.  We  recur  to  the  fact  that  the  rate  of 


366  NATURE    OF    CAPITAL   AND    INCOME 

interest,  in  the  price  sense,  was  defined  as  the  ratio  of 
income  to  capital,  when  the  first  installment  of  income  is 
due  at  the  end  of  the  first  time-interval.  But  if  the  first 
installment  is  due  at  the  beginning,  the  ratio  of  income  to 
capital  is  110  longer  the  rate  of  interest,  but  may  be  called  a 
sort  of  rate  of  discount. 

Thus,  if  $100  will  buy  a  perpetual  annuity  of  $4  a  year,  the 
first  installment  being  due  one  year  hence,  then  $  104  will  buy 
such  a  perpetual  annuity,  the  first  installment  being  due  at 
once.  In  the  first  case,  the  ratio  of  income  to  capital,  T^7,  is 
called  the  "rate  of  interest  in  the  price  sense."  In  the  second 
case,  the  ratio  of  income  to  capital,  T^¥,  may  be  called  "the  rate 
of  discount  in  the  price  sense."  The  rate  of  discount  in  the 
price  sense  and  the  rate  of  discount  in  the  premium  sense  are 
related  in  a  manner  strictly  analogous  to  the  relation  between 
the  rates  of  interest  in  the  two  respective  senses. 

As  is  well  known,  bonds,  just  before  an  installment  of 
interest  is  due,  are  sold  in  either  of  two  ways :  they  may  be 
sold  without  the  interest  payment  ("ex-interest"),  or  with  the 
interest  payment  ("fiat").  These  two  methods  are  associated 
respectively  with  the  rate  of  interest  and  rate  of  discount,  as 
just  described. 

§  7  (TO  CH.  XII,  §  7) 

Mathematical  Relations  between   the   Rates  of  Discount  for  Different 
Time  Reckonings 

The  rates  of  discount  for  different  time  reckonings  are 
related  in  a  manner  quite  analogous  to  that  in  which  the  corre- 
sponding rates  of  interest  are  related,  as  shown  in  this  Appen- 
dix, §  2.  Thus  if  V  to-day  will  buy  W  in  half  a  year, 

F_1      d' 
W~     ~Y' 

and  if  W  will  then  buy  V  in  another  half  year  on  the  same 
terms, 

IF_,      d' 
V'~     ~~2' 

V      f        (I '  \ 2 
whence,  multiplying,         — -  =  f  1  — -  ] . 

V      \         2 ) 


APPENDIX   TO   CHAPTER   XII  307 

But  —  =  1  —  d, 

therefore  1  —  d  =  (  1 

V         2 

and  d  =  d'-f~ 

from  which  we  see  that  the  discount  rate  reckoned  annually 
is  less  than  its  equivalent  reckoned  semi-annually.  Similar 
reasoning  applies  to  quarterly  and  other  rates. 

§  8  (TO  CH.  XII,  §  8) 
Dimensions  of  the  Rates  of  Interest,  Discount,  and  Capitalization 

The  rate  of  interest  in  the  price  sense  is  of  the  form  — 

Vt' 

where  v  represents  the  part  of  the  perpetual  income  stream 
which  flows  in  the  time  t,  and  V  represents  its  capital  value. 
Since,  in  this  fraction,  v  and  V  are  of  the  same  dimension, 
both  being  measured  in  dollars,  or  else  in  bushels,  or  in  some 
other  units  of  same  denomination,  the  dimensionality  of  the 

v  1 

fraction  —  reduces  to  -  or  t'1.*     In   like  manner,    the   ratio 

r  v  l> 

of  capitalization,  being  the  reciprocal  of  this  fraction,  or  — 

v  ' 

has  the  dimensionality  t. 

These  results  are  recognized  in  common  usage,  inasmuch  as 
the  rate  of  interest  is  so  much  per  annum,  and  the  ratio  of 
capitalization  is  so  many  years'  purchase. 

The  same  dimensionality  is  obtainable  from  the  rate  of 
interest  considered  as  a  premium.  The  rate  of  interest  as  a 

V 
premium  is  given  by  the  equation  —  =  (1  +  ti),  where  V  and 

V  are  two  exchangeable  sums  separated  by  the  interval  t, 
usually  a  fraction  of  a  year,  for  which  the  rate  of  interest  is 
to  be  reckoned.  Thus,  if  the  reckoning  is  quarterly,  t  is  \. 

V 
Since  V  and  Fare  of  the  same  dimension,  —  is  a  pure  number. 

*  It  is  interesting  to  observe  that  the  dimensionality  of  this  "price  of 
capital"  is  entirely  different  from  the  dimensionality  of  the  price  of  one 
kind  of  goods  in  terms  of  another,  as  shown  in  the  Appendix  to  Chap.  I. 


368  NATURE   OF   CAPITAL   AND    INCOME 

Hence  its  equal,  1  —  ti,  is  a  pure  number.     Since  of  this  sum, 
the  term  1  is  a  pure  number,  the  other  term,  ti,  is  also  a  pure 

number.     Hence  i  must  be  of  a  dimension  reciprocal  to  t,  i.e.  -, 

or  t~\ 

The  rate  of  discount  evidently  has  the  same  dimensionality 
as  the  rate  of  interest. 

APPENDIX  TO  CHAPTER  XIII 

§  1  (TO  OH.  XIII,  §  1) 
Formula  for  Present  Value  of  Sum  due  in  One  Year 

If  the  rate  of  interest  be  denoted  by  i,  it  is  evident  that  1  +  i 
due  next  year  is  worth  $  1  to-day, 

hence  $  1  due  next  year  is  worth  to-day, 

1  +  i 

and  any  sum  V  due  next  year  is  worth  :  to-day, 

J.  -f-  i 

which  is  the  general  formula  for  the  present  value  of  a  single 
sum  due  at  the  end  of  one  year. 


§  2  (TO  CH.  XIII,  §  1) 
Formula  for  Present  Value  of  Sum  V  due  at  End  of  Any  Time  t 

In  general,  it  is  obvious  that  (1-f  i)2  is  the  amount  which, 
two  years  hence,  has  a  present  value  of  $  1,  hence  that 

$1  due  at  the  end  of  2  years  is  worth  to-day 


and  that     V  due  at  the  end  of  2  years  is  worth  to-day  - —    .  .,. 

Similarly,  V  due  at  the  end  of  3  years  is  worth  to-day  — —  .  ,; 

(i  +  O 

and  V  due  at  the  end  of  t  years  is  worth  to-day  - 

(l  +  O' 

The  last  formula  is  perfectly  general.  It  is  not  even  nec- 
essary that  t  should  be  an  integer.  The  reader  who  is  mathe- 
matically inclined  will  have  no  difficulty  in  proving  that  the 
formula  applies  if  the  period  of  time  is  3^  years  or  any  other 
time  whatever. 


APPENDIX    TO    CHAPTER    XIII  369 

§  3  (TO  CH.  XIII,  §  3) 

Formula  for  the  Present  Value  of  a  Perpetual  Annuity 
The  proposition  that  the  present  value  of  a  perpetuity  is 

-  was  proved  in  the  preceding  chapter.  An  alternative  proof, 
i 

and  the  one  which  is  usually  given  in  treatises  on  annui- 
ties, is  as  follows :  Consider  a  perpetual  annuity  of  $  1 
per  annum ;  it  is  required  to  find  the  capital  value.  It  is 
evident  from  what  has  preceded  that  the  first  payment, 
$1,  being  due  at  the  end  of  a  year,  has  a  discounted 

value  at  the  present  time  of :;  the  second  has  a  present 

worth  of  -;  the  third, :  and  so  on  indefinitely. 

(1  +  i)2  (1  +  0 

Therefore,  the  present  value  of  the  entire  series  will  be, — 

1 H h  etc.,  ad  inf. 

i+r  (i  +  O*    (i+0a 

If,  for  brevity,  we  substitute  v  for :,  this  may  be  written, 

J.  -p  t 

v  +  v2  +  vs  +  ad.  inf., 
or  v  ( 1  +  v2  +  ad.  inf.) . 

Since  the  series  evidently  converges,  the  parenthesis  is  equal 

to  ,  which  may  be  seen  by  simply  dividing  1  by  1  —  v. 

1  —v 

Hence  the  value  of  the  annuity  is,  v 


l-v 
which  reduces  to  —  if  we  substitute  for  v  its  original  value, 


i  1  +  i 

This  sum,  -  dollars,   is,   therefore,    the    capital-value   of    an 
i 

annuity  of  $1.     By  proportion,  the  capital-value  of  any  other 
annuity  a  is  ~. 

§  4  (TO  CH.  XIII,  §  3) 

Formulae  and  Diagrams  for  Capital-value  of  Annuities  payable  Annually. 
Semi-annually,  Quarterly,  Continuously 

In  case  the  annuity  accrues  semi-annually,  the  teeth  will  be 
finer,  but  twice  as  frequent.     In  Figure  34  we  see  the  behavior 

2B 


370 


NATURE    OF    CAPITAL   AND    INCOME 


of  the  capitalized  annuity  if  the  annuity  is  payable  annually, 
semi-annually,  or  quarterly.  If  the  annuity  be  $4  a  year,  the 
teeth  drop  $4  if  payable  annually,  $2,  if  semi-annually,  and  $1, 
if  quarterly.  If  the  frequency  of  the  installments  of  income  be 


Semi-annual    Payments 


Quarterly   Payments 
FIG.  34. 

indefinitely  increased,  we  reach  the  limiting  case  of  a  continuous 
income,  when  the  teeth  disappear  entirely  and  the  value  of  the 
annuity  remains  at  a  constant  level.  The  value  of  the  annuity 
of  $4  in  all  these  cases,  just  after  any  installment  of  in- 
come is  received,  will  be  $100,  if  the  rate  of  interest 
is  4%,  provided  the  rate  is  respectively  "  reckoned  annually," 
semi-annually,  and  quarterly  in  the  various  cases.  In  the 
case  of  continuous  income,  the  value  of  the  annuity  of  $4 
will  ahvays  be  $100  if  the  rate  of  interest  be  4%  "reckoned 
continuously."  The  same  remarks  apply,  of  course,  to  an 
annuity  of  any  number  of  dollars.  Its  value  after  each  install- 
ment is  equal  to  the  annual  income  divided  by  the  rate  of  in- 
terest, or  the  annual  income  multiplied  by  the  purchase  period. 
In  order  to  obtain  the  formulae  for  the  value  of  a  perpetuity 
payable  semi-annually,  quarterly,  or  continuously,  in  terms  of  i, 
the  rate  of  interest  reckoned  annually,  we  need  only  to  transform 

-;-,  — ,  -,  by  means  of  the  equations  in  the  previous  chapter.    Thus 

I       %         O 


APPENDIX    TO    CHAPTER    XIII 


371 


the  value  of   an  annuity  of  a  dollars  per  annum  payable  semi- 

annually  is  ^  which,  by  substituting  for  i'  its  value  as  derived 

1  f         j'V 

from  the   relation  between  i  and  i',   viz.  1  +  i  =  ( 1  +  - ) ,  or 

\         »/ 

i'  =  2(Vl  +  i  —  1)  becomes     —  Similarly,   the 


-,  and  the  continuous 


quarterly  annuity  becomes 


annuity,  since  l+i=es  or  8=loge(l  +  t),  becomes -= 

8     lo& 

In  every  case  the  value  just  before  an  installment  is  found  by 
adding  that  installment  to  the  results  just  derived;  and  the 
value  at  intervening  points  by  applying  the  discount  curve, 
i.e.  dividing  the  impending  value  (just  before  the  next  in- 
stallment) by  (1  +  i)',  where  t  is  the  time  between  the  present 
and  the  time  of  the  next  installment. 

§  5  (TO  CH.  XIII,  §  3) 
Diagrams  for  Discontinuous  and  Continuous  Income 

If  the  income  installments  recur  annually,  and  are  $4  each, 
these  installments  are  represented  in  the  line  method  by  a,  a,  a, 


a 

a 

a 

b 

b 

b 

b 

b 

b 

c 

c 

c 

c 

c 

c 

c 

c 

c 

c 

c        c 

FIG.  85. 


in  Fig.  35.    If  they  occur  semi-annually,  in  installments  of  $  2 
each,  they  are  represented  by  6,  b,  b.     If  they  occur  quarterly,  in 


372 


NATURE    OF    CAPITAL    AND    INCOME 


installments  of  $  1  each,  they  are  represented  by  c,  c,  c,  and  so 
on  indefinitely,  in  each  case  the  lines  becoming  shorter  but  more 
numerous.  If  this  process  is  continued  indefinitely,  it  is  clear 
that  continuous  income  would  simply  be  represented  by  an  in- 
finite number  of  infinitesimally  small  lines, — a  representation 
which  would  be  unintelligible.  It  is  for  this  reason  that  the  area 
method  becomes  necessary.  To  show  how  it  may  be  used,  even 
for  discontinuous  income,  let  a  series  of  annual  payments,  a,  be 
represented  in  Figure  36  by  the  rectangles  whose  bases  are  equal 
to  unity  and  whose  altitudes,  therefore,  are  equal  to  a.  The  point 
of  time  to  which  each  rectangle  is  referred  is  taken,  for  conven- 
ience, as  the  end  of  each  year  in  which  it  occurs.  Thus  the  rec- 
tangle 0  V  refers  to  the  point  of  time  P,  and  P  W  to  Q.  If  the 
payments  are  semi-annual,  we  represent  them  by  the  areas  of 


U     V 


W 


D      X      Y      Z      P                           Q 
FIG.  36. 

the  rectangles  OT,  YV,  etc.,  in  the  same  manner.  But  as  the 
rectangles  are  each  equal  to  one  half,  the  altitudes  will  no 
longer  represent  the  individual  payments,  but  double  those  semi- 
annual payments,  i.e.  the  per  annum  rate.  Thus,  if  the  annu- 
ity is  $4  per  annum  payable  serni-annually,  the  rectangle  OT 
means  $2,  its  base  is  one  half,  and  its  altitude,  YT,  will  not  be 
2,  but  4,  the  rate  per  annum. 

Similarly,  quarterly  payments  are  represented  by  rectangles 
OS,  XT,  YU,  etc.,  whose  altitudes  will  again  represent  the  rate 
per  annum  of  each  quarterly  payment. 

Finally,  for  continuous  payments,  we  shall  have  an  infinite 
number  of  infinitesimal  rectangles,  forming  in  the  aggregate 
the  whole  figure  represented,  the  altitude  of  which  at  any  point 
will  be  the  rate  per  annum  at  which  income  is  flowing  at  that 
point. 


APPKNDIX    TO    CHAPTKR    XIII 


By  limits  we  may  pass  from  income  which  flows  at  a  uniform 
rate  to  any  income  stream.  Evidently,  therefore,  any  con- 
tinuous income-stream  may  be  represented  by  a  curve  (Fig.  37) 
of  which  the  ordinate  represents  the  per  annum  rate  of  flow  at  any 


point  of  time,  and  the  area  EC  between  any  two  ordinates  BE 
and  CF  represents  the  total  income  which  flows  within  the  time 
intercepted  between  those  ordinates. 

For  the  case  of  uniform  flow,  the  continuous  income  stream 
is  represented  in  Figure  38  by  the  area  OB.     OA  represents  the 


FIG.  38. 

rate  of  income,  and  OC  represents  the  capital-value  of  this  in- 
come.     This  capital-value  remains  constant,  as  shown  by  the 


374  NATURE   OF   CAPITAL   AND    INCOME 

horizontal  line  CD,  and  the  rate  of  interest  (reckoned  continu- 

is  ~oc 

§  6  (TO  CH.  XIII,  §  5) 
Formula  for  Capital-value  of  a  Terminable  Annuity 

Let  a  represent  the  annual  payment  of  the  annuity,  t  its 
duration  or  term,  and  V  its  present  value.  We  are  required 
to  find  V  in  terms  of  a,  i,  and  i,  the  rate  of  interest.  We 
have  observed  that  a  man  who  owns  such  a  terminable 
annuity  owns  the  difference  between  a  perpetual  annuity  be- 
ginning at  present  and  another  perpetual  annuity  deferred  t 
years.  Consequently,  the  value  of  his  property  is  the  differ- 
ence between  the  values  of  these  two;  that  is,  it  is  equal  to  the 
value  of  a  perpetual  annuity  beginning  now,  less  the  present 
value  of  a  perpetual  annuity  beginning  t  years  hence.  The 
deferred  annuity  which  begins  at  the  end  of  t  years  will,  we 

know,  be  worth  then  the  sum  of  -,  and  will  be  worth  now  what- 

i 

ever  is  the  present  value  of  this  -.      This  present  value  is  of 

i 

course  found  simply  by  discounting  the  -  just  obtained,  and  is 

i 


,-.  .y-  This  expression  should  therefore  be  subtracted  from 
the  value  of  the  other  perpetual  annuity  which  begins  now,  of 
which  the  present  value  is  ®.  This  subtraction  gives  the 

formula, 


§  7  (TO  CH.  XIII,  §  5) 

Discussion  of  Formulae   for  Terminable  Annuity  by  Diagrams.    "Total 
Discount."     "  Total  Interest."     Depreciation. 

In  Figure  39  let  AB  represent  the  term  t  of  the  annuity,  AD 
the  value  of  a  perpetual  annuity  beginning  at  the  point  of  time 
A,  and  BE  the  equal  value,  taken  at  the  end  of  the  term,  of  a 
deferred  perpetual  annuity  beginning  at  that  time.  Now  the 


APPENDIX   TO    CHAPTER    XIII 


375 


FIG.  39. 


present  value  at  time  A  of  the  value  BE,  at  time  B,  is  evi- 
dently AC,  found  by  drawing  the  discount  curve  CE.  There- 
fore the  value  of  the  terminable  annuity  is  equal  to  AD  —  AC, 


376 


NATURE   OF   CAPITAL   AND   INCOME 


or  DC,  which  is  the  total  discount  on  BE;  i.e.  the  amount  by 
which  it  is,  as  Bdhm-Bawerk  says,  "  diminished  in  time  per- 
spective." 

Similarly,  the  capital-value  of  the  annuity,  taken  at  any  time 
later  A  (just  after  an  installment  of  income),  is  equal  to  the 


smaller  sum  GH.  Thus  the  capital-value  gradually  decreases 
in  accordance  with  the  distance  of  the  curve  CE  from  the 
line  DE. 

In  this  representation  the  discount  curve  was  drawn  through 
E.  If  another  is  drawn  through  D  it  may  be  shown  that  EF 
is  the  "amount"  of  the  terminable  annuity,  or  its  value  at  the 
time  it  terminates,  if  we  suppose  that  each  individual  item  is  put 
at  interest  from  its  date  to  the  point  of  time  B.  This  "amount," 
EF,  is  called  the  "total  interest"  on  that  capital  in  that  interval. 

In  the  same  way,  at  any  intermediate  time  just  after  an  install- 
ment, GI  will  represent  the  value  of  the  annuity  concentrated 
at  that  point,  and  this  value  will  consist  of  two  parts,  HG, 
which  is  the  (discounted)  value  of  the  part  subsequent  to  A", 
and  ///,  the  (accumulated)  value  of  the  part  preceding  K. 


APPENDIX    TO    CHAPTER    XIII 


377 


The  decrease  in  capital-value  of  the  annuity,  which  has  been 
represented  by  the  approach  of  CE  to  the  horizontal  line  DE 
above  it,  is  better  represented,  however,  by  inverting  CE  to 
the  position  KB,  in  order  that  the  capital-value  may  be  repre- 
sented, as  in  our  previous  examples,  by  the  distance  from  the 


FIG,  41. 


horizontal  line  AB  below  it.  This  change  is  accomplished 
in  Figure  40.  The  value  of  the  annuity  taken  after  each 
installment  of  income  is  represented  by  the  ordinate,  as  mA', 
of  the  curve  KB,  and  the  value  just  before  an  installment 
is  represented  by  the  ordinate,  as  nA",  of  a  point  above  this 
curve  a  distance  equal  to  that  installment.  The  value  at  inter- 
mediate points  evidently  follows  a  discount  curve,  as  mn,  be- 
tween these  two  points.  The  result  is  that  the  capital-value 
will  rise  and  fall  according  to  the  steps,  or  teeth,  shown  in  the 
diagram. 

As  the  income  items  become  more  numerous  the  teeth  be- 
come more  frequent  and  smaller,  and  disappear  Avhen  the  flow 
of  income  is  continuous,  as  represented  in  Figure  41,  where  the 


378  NATURE    OF   CAPITAL   AND    INCOME 

curve  KB  itself  represents  the  capital-value  at  all  points  of 
time. 

The  formula  for  the  present  value  (V)  of  the  annuity  just 
after  each  installment  of  income  is  the  same,  whatever  the 
time  intervals  between  installments.  This  is  strictly  true,  how- 
ever, only  on  the  proviso  that  the  rate  of  interest  i  is  to  be 
understood  as  reckoned  in  accordance  with  the  frequency  of 
the  installments  of  income  in  each  case,  —  semi-annually,  quar- 
terly, etc.,  —  instead  of  annually,  as  has  been  hitherto  under- 
stood. 

The  formula  for  the  capital-value,  V,  just  before  an  install- 
ment is  evidently  found  by  taking  the  preceding  formula  for 
V  and  adding  a.  This  gives,  — 

a 

-  -       i        +  a. 

At  intermediate  points  the  capital-value  is  equal  to  the 
amount  just  named  discounted  for  the  interval  elapsed  be- 
tween the  point  of  time  considered  and  the  next  installment 
of  income. 

§  8  (TO  CH.  XIII,  §  7) 
Formulae  for  Value  of  a  Bond 

To  be  general,  let  us  suppose  a  bond,  the  income  from  which 
is  a  dollars  per  year,  payable  annually  for  t  years,  at  the  end  of 
which  time,  in  addition  to  the  final  payment  a,  another  larger 
payment  P,  called  "  principal, "  is  paid.  We  are  required  to 
find  the  present  value,  V,  of  these  future  expected  payments 
for  a  given  rate  of  interest,  i. 

The  discounted  value  of  the  terminable  annuity  has  already 
been  expressed,  namely, — 

a 
a  i 

The  discounted  value  of  P  deferred  t  years  has  also  been 
explained  and  is  evidently, — 

P 


APPENDIX    TO    CHAPTKR    XIII  379 

The  sum  of  these  expressions  is  the  value  F",  which  we  are 
seeking.     In  other  words, — 

a 
y__  a  i  P 

~~ 


or 


i      (1  +  0* 

Some  special  cases  may  be  considered.  First,  if  the  annual 
income  a  is  the  interest  on  the  "  principal "  P,  —  i.e.  if  a  =  Pi 

( orP=-  j, — the  second  term  vanishes,  as  its  numerator  is 
evidently  zero,  and  since  the  first  term,  -,  is  by  present  hy- 

t> 

pothesis  P,  the  equation  then  becomes   V=  P. 

Secondly,  if  a  is  greater  than  iP,  it  may  be  readily  shown  that 
V  will  be  greater  than  P;  and  if  a  is  less  than  iP,  that  V  is 
less  than  P. 

The  formula  given  is  of  practical  importance,  as  it  enables 
us  to  compute  the  price  at  which  a  bond  must  sell  in  order  to 
yield  a  certain  rate  of  interest. 

To  apply  the  formula  numerically  we  need  only  to  assign 
particular  values  for  the  magnitudes  involved.  Let  us  take  the 
numerical  case  already  considered,  where  P=$100,  a  =  $5, 
i=.04,  and  t  =  W.  In  this  case  the  formula  becomes, — 

5 

...          100         7T7 


.04^    (1.04)1" 
which  reduces  to  108,  as  we  found  before. 

Similarly,  it  may  be  shown  that  if  bonds  are  sold  on  a  6  % 
basis,  the  price  of  the  bond  in  question  would  be  $92.V. 

We  have  derived  the  value  of  a  bond,  I",  just  after  a 
payment  of  "interest."  In  this  case  the  bond  is  said  by 
brokers  to  be  sold  "ex-interest."  If,  on  the  contrary,  it  is 
sold  "  flat,"  that  is,  with  interest,  its  value  will  evidently  be 
increased  by  the  "  interest "  a,  and  Avill  be  V+  a.  The  price 

at  any  time  between  installments  will  evidently  be  -         '— , 

J  (1-HV 


380  NATURE    OF   CAPITAL   AND    INCOME 

where  V  represents  the  value  the  bond  will  have  after  the  next 
"interest"  payment,  and  t'  the  time  elapsing  to  that  payment. 
Or,  it  is  V(l  +  iy",  where  V  represents  the  value  after  the 
last  "interest"  payment,  and  t"  the  time  since  said  payment. 
Practically  this  last  formula  reduces  to  V  -\-  Vit",  which  in  turn 
is  practically  the  same  as  V-\-  at"  ;  for  a  and  Vi  are  practically 
equal,  each  being  nearly  the  true  interest  for  one  installment 
period.  This  is  the  formula  usually  employed  by  brokers,  at" 
being  called  the  "  interest  earned  "  since  the  last  coupon. 

§  9  (TO  CH.  XIII,  §  7) 

Alternative  Method,  whereby  the  "Premium"  in  the  Price  of  the  Bond 
is  compounded  separately 

The  so-called  5  °/0  bond  running  for  10  years,  which  is  sold 
on  a  basis  of  4  %,  may  be  considered  as  consisting  of  the  follow- 
ing two  property  rights :  (1)  the  right  to  four  dollars  a  year 
for  10  years  and  $100  at  maturity,  and  (2)  the  right  to  one 
dollar  a  year  for  10  years.  It  is  evident  that  the  present 
value  of  the  first  property  is  $  100,  to  which,  therefore,  we  need 
only  to  add  the  value  of  the  second  property,  namely,  the  an- 
nuity of  $  1  a  year  for  10  years.  It  is  therefore  the  present 
value  of  this  small  annuity,  consisting,  we  may  say,  of  the 
difference  between  the  real  and  nominal  interest  on  $100, 
which  constitutes  the  "premium"  on  the  price  of  the  bond. 
This  present  value  is  $8,  and  is  found  in  the  manner  already 
explained  for  terminable  annuities,  being  the  total  discount  on 
$25  at  the  end  of  10  years,  $25  being  the  capital-value  of  a 
perpetual  annuity  of  $1  a  year,  when  interest  is  reckoned  at 
4  °J0-  Consequently,  the  bond  is  worth  in  all  $108.  This  value 
is  represented  diagrammatically  in  Figure  42. 

Let  A  A'  represent  the  10-year  period,  with  the  $5  interest 
payments  shown  by  the  ten  vertical  lines  at  unit  intervals. 
A'B'  represents  the  $100  "principal"  due  in  10  years,  and 
AB  represents  what  the  bond  would  be  worth  ($100)  if  the 
interest  payments  were  $4  instead  of  $5.  To  this  must 
therefore  be  added  the  present  value  of  $1  a  year  for  10  years. 
This  is  the  total  discount  on  B'C'  (drawn  equal  to  $25),  the 
capitalization  of  a  perpetual  annuity  of  $  1  a  year.  The  total 


Ari'KXDIX    TO    CHAPTKR   XIII 


381 


discount  on  this  .$-«">  is  shown  by  the  line  ED,  which  is  there- 
fore the  premium  in  the  selling  price  of  the  bond.  The  total 
price  is  AB  +  BD  =  A1).  The  price  at  later  dates  (taken 
each  just  before  an  installment)  is  represented  by  points  on 


|5          15 


J5          |5          |5          |5          |5 


25 


100 


A' 


FIG.  42. 


the  discount  curve  DB'  drawn  with  reference  to  CC'  as  a 
horizontal  axis.  Adding  at  each  of  these  installment  points  a 
line  equal  to  §5,  we  have  the  value  just  before  interest  pay- 
ments, and  connecting  the  tops  of  these  lines  with  the  preceding 
interest  intervals  by  discount  curves  reckoned  at  4%,  we  have 
a  series  of  teeth  representing  the  normal  course  of  the  price  of 
the  bond  from  the  present  to  maturity. 

In  case  a  bond  is  sold  at  a  G%  basis,  we  have  the  curve  B'D', 
instead  of  B'D,  with  the  teeth  superimposed  as  before,  the 
tooth  curves,  however,  being  in  this  case  on  a  6%  slope. 


382  NATURE   OF   CAPITAL   AND   INCOME 

§  10  (TO  CH.  XIII,  §  7) 
Formula  for  a  Bond  when  Interest  is  reckoned  oftener  than  yearly 

The  formula  in  the  case  of  semi-annual  income  when  in- 
terest is  reckoned  semi-annually  is  evidently, — 

p_  a 


which  applies  just  after  an  interest  payment;  just  before,  it 
is  evidently  F+^;  and  at  intervening  intervals  it  is  this  value 


discounted,  or  for  practical  purposes,  the  simple  formula, 
V+at',  where  V  is  the  value  taken  after  the  last  "interest" 
payment,  and  t  the  time  elapsing  since  that  date.  For  the  case 
of  continuous  interest,  if  we  let,  as  in  the  previous  chapter, 
8  represent  continuous  interest,  we  have,  — 


8  ets 

which  formula  remains  unchanged  during  the  entire  period  of 
the  bond. 

These  various  formulae  may,  of  course,  be  somewhat  trans- 
formed and  simplified  for  practical  purposes.  Moreover,  they 
may  all  be  transformed  in  terms  of  the  various  rates  of 
interest.  Some  actuaries  apparently  prefer  to  use,  as  the  in- 
terest rate,  only  the  "effective"  rate,  i,  which  is  what  we  call 
the  "rate  of  interest  reckoned  annually."  The  preceding 
formulae,  which  employ  the  semi-annual,  quarterly,  and  other 
forms  of  interest  rates,  may  be  transformed  by  substituting 
their  values  in  terms  of  z,  in  accordance  with  the  relations 
shown  in  Appendix  to  Chap.  XII,  §  2. 

§  11  (TO  CH.  XIII,  §  8) 
Formula  for  Capital-value  of  Any  Series  of  Income  Installments 

We  may  express,  in  general  formulae,  the  capital-value  of 
any  income  stream,  as  follows  :  Let  a,,  a,,  n>:!,  represent  the 
successive  installments  of  income  accruing  at  various  times  dis- 


APPENDIX    TO    CHAPTER   XIII  383 

tant  from  the  present  instant  by  the  intervals  tlf  t,,,  t.A,  etc.,  which 
may  be  equal  or  unequal,  whole  or  fractional,  or  even  positive 
or  negative  according  as  the  income  is  in  the  future  or  in  the 
past.  Let  t  represent  the  rate  of  interest.  The  present  value 
of  such  an  income  stream  will  be, — 

^=(lf7)T,  +  (lf77,  +  (lf;7.  +  'etc- 

Or,  in  briefer  notation, 

where  2  is  taken  in  its  usual  sense  of  the  summation  of  the 
series  of  terms  of  the  type  of  that  following  it. 

§  12  (TO  CH.  XIII,  §  8) 

Diagram  and  Formula  for  deriving  Capital-value  from  a  given  Continuous 
Income  Stream 

For  any  income  stream  flowing  continuously,  and  represented 
in  Figure  43  by  the  area  below  MN,  the  capital-value  will 
be  represented  by  the  curve  NO.  The  ordinate  of  the  income 
stream  at  any  point,  as  RS,  represents  the  rate  of  its  flow  at  that 
point,  and  any  area,  as  RSS"R",  represents  its  total  flow  through 
the  period  RH".  The  ordinates  of  the  curve  NO  will  repre- 
sent the  capital-value  of  this  income  stream.  NO  is  con- 
structed from  N  backward  as  follows  :  the  curve  begins  at  N 
on  the  income  stream  and  is  generated  by  a  point  moving  in 
such  a  manner  that  at  any  position  0  its  direction  of  motion 
is  the  resultant  of  two  tendencies.  To  represent  these 
two  tendencies  we  draw  through  0  the  discount  curve  OP. 
Tangent  to  this  curve  we  draw  OH  so  as  to  meet  the  line  QH 
drawn  vertically  and  distant  to  the  left  one  unit  from  OK. 
OH  represents  one  of  the  two  tendencies  mentioned,  that  due 
to  discounting  the  future.  OK  drawn  vertically  up  from 
and  equal  to  ItS,  the  rate  of  income  at  that  time,  represents 
the  other  tendency.  The  resultant,  OQ,  drawn  according  to 
the  principle  of  the  parallelogram  of  forces,  will  represent  the 
actual  direction  in  which  the  curve  will  be  moving  at  the 
point  0.  In  other  words,  a  point  moving  under  the  influ- 
ence of  two  forces,  OK  and  OH,  will  generate  the  required 
curve  NO. 


NATURE    OF   CAPITAL   AND    INCOME 


In  order  to  show  that  this  is  a  correct  representation  let  us 
first  take  the  case  of  semi-annual  income.  RR"  represents  one 
year ;  Rr  represents  half  a  year.  Draw  the  ordinate  rh.  From 
h  draw  vertically  upward  hq  to  represent  a  half-year's  install- 
ment of  income,  that  is,  half  of  Rs.  To  avoid  complicating  the 
figure,  hq  is  omitted;  were  it  drawn,  q  would  lie  on  the  line  OQ'. 
Then,  according  to  our  previous  representation,  the  capital- 
value  will  follow  the  curve  Ohq,  which  forms  a  "tooth."  The 
line  Oq  is  therefore  a  line  drawn  through  the  top  points  of  two 
neighboring  teeth.  Its  direction  is  a  first  approximation  to 


R"/'    R 


FIG.  43. 


the  direction  OQ  of  the  curve  for  the  continuous  case.  This 
direction  Oq  is  the  diagonal  of  a  parallelogram  formed  by 
producing  Oh  to  meet  the  ordinate  from  R"  in  //',  producing 
Oq  to  Q'  and  completing  the  parallelogram. 

Since  H'Q'  is  twice  as  far  from  0  as  hq  (i.e.  RR"  =  2  (rR) 
by  hypothesis),  it  follows,  by  similar  triangles  (i.e.  Ohq  and 
0//'Q'),  that  it  is  also  twice  as  long.  But  hq  represents  a 
half  year's  installment  of  income.  Hence  H'Q'  represents  two 


APPENDIX    TO    CHAPTER    XIII 


385 


such,  installments,  or  the  annual  rate  of  income.  Therefore 
OK,  being  of  the  same  length,  also  represents  this  annual  rate 
of  income. 

In  other  words,  the  direction  from  0  to  q  lies  along  a  paral- 
lelogram of  which  the  side  OK  represents  the  annual  rate 
of  income  and  the  side  OH'  a  chord  of  the  discount  curve 
OP. 

Now  it  is  evident  that  if,  instead  of  a  semi-annual  installment, 
we  assume  greater  frequency,  the  same  statement  will  apply 
except  that  the  point  h  will  be  nearer  0,  By  proceeding  in  this 


FIG.  44. 

manner  the  chord  Oh  If  approaches  the  tangent  OH  as  its 
limit,  and  the  parallelogram  OH'Q'K  becomes  at  the  limit 
the  parallelogram  OHQK  as  originally  described.  That  is,  its 
sides  are  0/v,  the  annual  rate  of  income,  and  OH,  the  tangent 
to  the  discount  curve  drawn  from  O  to  a  vertical  line  one  year 
to  the  left. 

That  this  construction  and  its  demonstration  bear  a  striking 
analogy  to  the  construction  and  demonstration  which  apply  to 
2c 


386 


NATURE   OF   CAPITAL   AND    INCOME 


the  composition  of  forces  or  motions  is  very  evident.  Availing 
ourselves  of  this  analogy,  we  may  say  that  in  the  case  of  dis- 
continuous income,  the  point  O  traces  the  capital  curve  (back- 
ward) by  obeying  alternately  two  tendencies,  —  one,  to  follow 
the  discount  curve  at  times  when  no  income  occurs,  and  the 
other,  to  rise  vertically  whenever  income  occurs.  In  the  case 
of  continuous  income  these  motions  occur  simultaneously 
instead  of  alternately,  and  the  resultant  is  a  smooth  curve 
instead  of  a  series  of  teeth. 

The  same  principles  apply  when  part  of  the  income  curve 
is  below  the  horizontal  axis,  representing  negative  income.     If 


FIG.  45. 


at  the  beginning  the  prospective  cost  just  counterbalances  the 
prospective  income,  the  capital-value  will  at  that  instant  be 
zero,  and  will  from  that  point  rise  and  fall  again  to  zero  at  the 
end,  as  indicated  in  Figure  44. 

The  formula  for  capital-value  in  the  case  of  a  continuous 
income  stream  will  be,  — 

da 


-  C 
~J 


in  which  da  may  be  said  to  represent  the  infinitesimal  income 
which  flows  in  the  infinitesimal  increment  of  time  dt.  In  other 
words,  da  represents  an  infinitesimal  element  of  the  area  ABC 
(Fig.  45),  of  which  element  the  base  or  breadth  represents  the  in- 
finitesimal time  dt.  For  the  purpose  of  integration  we  may  sub- 
stitute for  da  the  expression  f(£)dt,  where/  (i)  represents  CB,  or 
the  ordinate  of  the  income  stream  taken  as  a  function  of  time  /. 
If  the  special  form  of  the  function  /(i)  is  known,  it  is  evidently 
possible  to  integrate  the  expression  and  obtain  its  value  for  any 
given  limits. 


APPENDIX    TO    CHAPTER   XIII 


387 


§  13  (TO  CH.  XIII,  §  8) 
Diagram  showing  the  Accumulated  "Amount"  of  a  Given  Income  Stream 

We  reproduce  in  Figure  4(5  the  diagram  with  which  we  began 
the  study  of  the  general  case  of  capitalizing  income.  We  now 
wish  to  obtain  the  accumulated  value  A'"Q,  at  the  close  of  the 
period  OA"',  of  the  income  items  AB,  A'B',  A"B",  and  A'"B"'. 


This  consists  of :  (1)  A"'B'"  itself  ;  (2)  B'"E,  which  is  the  amount 
of  C"D"  (or  its  equal,  A"B"),  and  is  found  by  continuing  the 
discount  curve  C'D"  to  E;  (3)  EF,  which  in  like  manner  is  the 
amount  of  CD'  (or  its  equal  A'B'};  and  (4)  FQ,  which  is  the 
amount  of  CD  (or  its  equal  AB).  Thus,  while  OP  represents 


38S  NATURE    OF    CAPITAL   AND    INCOME 

the  price  of  the  stream  if  paid  for  in  advance,  A'"Q  repre- 
sents the  price  if  paid  for  at  the  end.  By  similar  reasoning 
it  may  be  shown  that  the  price  at  any  intermediate  point  of 
the  entire  series  is  the  height  of  any  point  on  the  one  smooth 
curve  PQ. 

This  result  must  not  be  confused  with  that  which  represents 
the  capital-value  of  future  income.  Thus,  at  the  point  of  time 
0',  the  line  O'P1  represents  the  value  of  all  the  income  items, 
past  as  well  as  future,  AB,  A'B',  A"B",  A"'B'",  whereas  the 
line  O'P"  represents  the  value  of  only  the  future  items  A"B" 
and  A'"B"'. 

§  14  (TO  Cn.  XIII,  §  10) 

Effect  of  reckoning  Semi-annually,  Quarterly,  and  Continuously,  on  the 
Rate  of  Interest  realized  on  a  Stock  or  Store  of  Articles 

As  usual,  the  passage  from  the  rate  of  interest  reckoned 
annually  to  the  rate  of  interest  reckoned  continuously,  if  accu- 
rately considered,  is  not  so  simple  as  appears  on  the  surface 
and  may  afford  to  some  readers  no  little  perplexity.  If  we 
assume,  for  convenience,  that  each  article  in  the  merchant's 
stock  remains  there  for  a  definite  period,  called  the  time  of 
"turn-over,"  and  the  cost  of  purchase  and  all  the  other  costs 
connected  with  the  article  occur  at  the  time  it  enters  the 
stock,  while  all  the  receipts  or  gross  income  from  that  article 
occur  at  the  time  that  it  leaves  the  stock,  we  may  pass  from 
the  case  of  the  rate  of  interest  "reckoned  annually"  to  that 
of  the  rate  of  interest  "  reckoned  continuously  "  as  follows :  — 

As  a  first  step  we  assume  that  all  of  the  stock  is  bought  at 
the  beginning  of  a  calendar  year  and  sold  at  the  end,  so  that 
the  time  of  turn-over  is  one  year.  If  the  cost  of  the  stock  is 
represented  by  c,  including  not  only  the  purchase  price  but  all 
other  elements  of  cost,  this  must  represent  the  discounted 
value  of  the  receipts  at  the  end  of  the  year,  which  are  there- 
fore c(l  +  ?').  The  net  income  for  the  year  is,  therefore, 
c(l-M)  —  c,  or  ci.  This  bears  a  ratio  to  the  total  cost  value 

reckoned  at  the  beginning  of  the  year,  namely  c,  of  — ,  equal 
to  the  rate  of  interest,  i. 

For  the  second  step  we  consider  the  stock  as  half  purchased 


APPKXDIX    TO    CHAPTER    XIII  389 

on  January  1  and  half  on  July  1,  six  months  later,  and  that, 
as  before,  each  element  of  the  stock  remains  one  year  before 

sale.     The  cost  on  January  1  is  -,  and  on  July  1  is  also  - 

—  £ 

If  we  take  inventory  on  July  1,  the  stock  just  purchased  rep- 

s* 

resents  a  value  -,  while  that  purchased  six  months  before,  and 

£i 

which  is  to  be  disposed  of  in  six  months  more,  may  be  taken 
as  having  a  somewhat  greater  value,  namely,  -  V  1  +  z  ,  the 

U 

latter  being  the  cost  value  plus  interest,  or,  what  amounts  to 
the  same  thing,  the  expected  selling  value  less  interest.  The 
total  stock  is  therefore  worth  on  July  1,  — 


2+<>V  1  -r  /. 

The  sales  or  receipts  from  the  stock  will  evidently  be  every  six 
months  -  (1-f  i),  this  being  the  accumulated  value  for  one 

a 

year  of  the  amount  purchased,  -.     For   the  entire   year  the 

receipts  will  thus  be  just  double,  or  c  (1  +  «').  If  from  this 
we  deduct  the  per  annum  cost,  c,  we  obtain,  as  before,  the 
net  income,  ci.  The  ratio  of  this  net  income  to  the  capital- 
value  taken  on  January  1  or  July  1,  of  any  year,  will  therefore 
be,  — 

ci 

c      c      - 
2      2  V  i  +  z' 

2i 


This  expression,  which  is  evidently  the  same  as 

1  +  V  1  +  i 

seems  no  longer  to  be  equal  to  the  rate  of  interest  ;  but  the  dis- 
crepancy is  due  to  the  fact  that  the  merchant's  income  accrues 
semi-annualty,  whereas  i  is  reckoned  annually.  If  we  substi- 
tute for  i  its  value  in  terms  of  i  ',  the  rate  of  interest  reckoned 

semi-annually  (namely,  i'-\  —    ,  as  shown  in  the  Appendix  to 

4 

Chap.  XII,  §  2),  we  shall  find,  on  simplifying,  that  the  above 
expression  reduces  to  <".  In  other  words,  in  the  artificially 
simple  case  in  which  the  merchant  is  supposed  to  accomplish 


390  NATURE    OF   CAPITAL   AND    INCOME 

all  his  buying  and  selling  in  two  equal  amounts  and  at  semi- 
annual intervals,  the  ratio  of  his  annual  income  to  his  capital, 
reckoned  at  these  times,  is  i '.  In  the  same  manner  it  may  be 
shown  that  if  his  buying  and  selling  take  place  at  quarterly 
intervals,  the  ratio  of  his  income  to  his  capital  reckoned  at  these 
times  will  be  i",  i.e.  the  rate  of  interest  per  annum  reckoned 
quarterly;  and  so  on  indefinitely  until  we  reach  the  limiting 
case,  approximately  true  in  practice,  in  which  the  merchant  buys 
and  sells  daily,  when  we  find  that  the  annual  net  income, 
divided  by  the  value  of  the  capital  at  any  instant,  is  equal 
to  the  rate  of  interest  reckoned  continuously.  It  will  be  observed 
that  to  make  this  proposition  .hold  good  it  is  necessary 
that  the  valuation  of  the  merchant's  capital  shall  be,  not 
its  wholesale  price  nor  its  retail  price,  but  something  inter- 
mediate, which  shall  take  account  of  the  fact  that  the  stock 
cannot  all  be  sold  immediately,  and  that,  on  the  other  hand,  it 
will  not  be  necessary  to  wait  a  year  before  it  is  all  sold.  Similar 
reasoning  may  evidently  be  applied  in  case  the  time  of  turn- 
over of  the  stock  is  more  or  less  than  a  year. 


§  15  (TO  CH.  XIII,  §  11) 
Influence  of  Variability  of  Rate  of  Interest 

Thus  far  we  have  treated  the  rate  of  interest  in  successive 
years  as  invariable.  As  a  matter  of  fact,  the  rate  of  interest 
is  constantly  fluctuating.  We  shall  suppose  at  first  that  these 
fluctuations  are  foreknown,  and  for  convenience  we  shall  confine 
ourselves  to  a  year  as  the  standard  interval  of  time.  Let  us 
assume  that  the  rate  of  interest  for  the  first  year  is  i1}  for  the 
second  year,  i<2,  for  the  third  year,  is>  and  so  on  indefinitely,  all 
of  these  being  supposed  to  be  known  in  advance.  By  means  of 
these  rates  of  interest  we  can  calculate  the  present  value  of 
any  item  or  series  of  items  of  income.  Thus,  if  f?1000  is  due 
in  two  years  and  the  rate  of  interest  for  the  first  year  (j'j)  is 
5%,  while  the  rate  for  the  second  year  (?2)  is  3%,  we  can 
obtain  the  present  value  of  the  $1000  by  discounting  it  at  3% 

for  one  year,  thus  obtaining ,  or  $970.87,  as   its  value    a 

l.Oo 


APPENDIX    TO    CHAPTER    XIII 


391 


year  previous  to  the  due  date,  or  one  year  from  the  present, 
and  rediscounting    this    970.87   at  5%   for  one  year,  giving 

Q"0  87 

'     ,  or  $924.30,  as  the  present  value. 
l.Uo 

In  general,  if  V  represents  the  item  of  income  to  be  received, 

T7" 

its  value  in  one  year  will  be  —      —  and  its  present  value, 

1  +  /, 

V 


(1  +  /,)(!  +  /,)' 

which  formula  is,  of  course,  easily  extensible  to  three  or  any 
number  of  years. 

If  we  represent  the  future  value  Fin  Figure  47  by  the  line 
AB,  its  value  in  one  year  is  CF,  found  by  the  3%  discount 


FIG.  47 


curve  BC,  and  its  present  value  is  ED,  found  by  the  5%  dis- 
count curve  DC.  In  other  words,  instead  of  having  a  uniform 
discount  curve  from  B  to  D,  we  have  a  broken  discount  curve 
BCD,  with  a  different  percentage  rate  of  rise  for  the  two 
years  considered. 

In  this  way  we  may  obtain  the  present  value  of  any  series  of 
income  items  precisely  as  before,  with  the  exception  that  the  dis- 
count curves  are  now  somewhat  irregular.  Thus,  if  the  series 
of  income  items  at  different  points  of  time  are  of  the  magnitude 


392 


NATURE    OF    CAPITAL    AND    INCOME 


represented  in  Figure  48  by  AS,  CD,  EF,  and  GH  (read  in  the 
order  of  futurity),  the  remotest  item,  AB,  is  discounted  by 
means  of  the  discount  curve  BC,  and  the  next  to  the  last  item 
is  added  to  the  capital-value  at  C,  bringing  the  capital-value  to 
the  point  D,  from  which  the  next  discount  curve  DE  is  drawn, 
and  so  on  until  we  reach  the  point  I.  IJ  is  thus  the  capital- 
value  of  the  given  series  of  income  items. 

In  this  way  it  is   possible  to  review   all  the  special  cases 
of  capitalizing  income  which  were  considered  in  Chapter  XIII, 


-iF 


FIG.  48. 


and  correct  them  for  the  general  case  of  a  rate  of  interest 
which  is  variable  but  foreknown.  Such  a  calculation,  how- 
ever, is  of  very  little  practical  consequence,  inasmuch  as  the 
variations  in  the  rate  of  interest  are  seldom  if  ever  foreknown. 
Were  it  worth  while  to  pursue  the  subject,  it  would 
be  convenient  to  simplify  the  calculations  by  substituting, 
where  possible,  for  the  series  of  rates  of  interest  il9  i.,, 
?'3,  etc.,  an  average,  .;',  such  that  if  the  given  series  of  in- 
come items  were  discounted  uniformly  according  to  the  rate 
of  interest  j,  we  should  obtain  exactly  the  same  present 
value  as  when  the  several  separate  rates  ?\,  i2,  ?3,  etc.,  are 
employed.  The  formula  for  the  average  rate  of  interest  j  of 


APPENDIX   TO    CHAPTER    XIII  393 

any  particular  number  of  individual  rates,  as  ij,  i'2,  ?3,  etc., 
used  for  discounting  individual  items  of  income,  cij,  a2,  a3, 
would  evidently  be, 

_OL_  a,  a, 

8 


-.  +  —  -^ — —  4- — ^ + . 


Various  applications  of  such  formulae  might  be  made,  though 
they  have  little  practical  utility.  Thus,  the  value  of  a  termi- 
nable annuity  of  a  given  term  is  found,  as  before,  by  taking  the 
difference  in  value  between  a  perpetual  annuity  beginning  to- 
day and  a  perpetual  annuity  deferred  to  the  end  of  the  given 
term.  The  value  of  the  perpetual  annuity  beginning  to-day 
would  be  found,  as  has  just  been  shown,  by  dividing  the  annual 
income  a  by  jlt  the  average  rate  of  interest  of  the  individual 
rates  from  the  present  into  the  indefinite  future.  The  value 
of  the  deferred  annuity  taken  at  the  end  of  the  term  would  be, 

in  like  manner,  — ,  where  jt  is  the  average  of  the  individual 

Jt 

rates  from  that  point  indefinitely  forward.  The  present  value 
of  this  deferred  annuity  would  be  found  by  discounting  the 
latter  value  for  the  term  of  the  annuity  according  to  the  rate 
jltt  where  jltt  is  the  average  of  the  individual  rates  of  interest 
h)  ''2?  *s>  .  •  .  t,  for  the  term  of  the  annuity. 

The  value  of  a  bond  would  be  found  in  a  similar  manner. 
We  have  just  shown  how  to  find  the  present  value  of  the 

"interest"  of  the  bond,  and  the  present  value  of  the  "princi- 

p 
pal,"  P,  due  at  maturity,  would  be  evidently  - : — . 


§  16   (TO  CH.   XIII,  §  11) 

Representation  of  Capital  and  Income  by  Polar  Coordinates 

The  mathematical  reader  may  be  interested  in  an  alternative 
method  of  representing  income  and  capital,  by  which  polar 
coordinates  are  employed  instead  of  rectangular.  Let  the 
radius  vector  in  Figure  49  represent  the  parent  capital.  The  time 
required  for  a  complete  revolution  of  the  radius  vector  may  be 


394  NATURE    OF   CAPITAL   AND    INCOME 

taken  to  represent  the  "  purchase  period. "  Thus,  if  the  rate  of 
interest  is  4  %,  the  purchase  period  is  twenty-five  years.  During 
one  year  the  radius  vector  will  move  through  an  angle  -^  of  a 


FIG.  49. 


complete  revolution,  and  the  length  of  the  radius  vector  will 
increase  from  OA  to  OB  by  an  amount,  BC,  -^  of  the  original 
OA,  interest  being  4  %  reckoned  annually.  In  case  the  inter- 
est BC  is  not  reinvested,  but  detached  from  the  principal,  next 


AI'I'KXDIX    TO   OHAITKR    XIII  305 

year  will  bring  the  radius  vector  to  the  position  OD,  at  which 
time  the  same  interest,  DE,  may  be  detached,  and  so  on  in- 
definitely, the  result  being  a  toothed  wheel.  Each  tooth  being 
^  of  the  radius  OA,  the  sum  of  the  twenty-five  teeth  will  be 
exactly  equal  to  the  radius.  In  case  the  interest  is  reckoned 
semi-annually,  the  teeth  will  be  fifty  in  number  instead 
of  twenty-five,  but  each  will  be  half  as  large;  and  so  on 
until,  for  "continuous"  reckoning,  we  have  an  infinite  number 
of  teeth  each  of  infinitesimal  size ;  but  the  sum  of  the  whole 
number  in  the  complete  revolution  will  still  be  exactly  equal 
to  OA. 

In  case  no  income  is  received,  the  accumulation  of  capital  is 
represented,  by  increasing  the  length  of  the  radius  vector,  the 
end  of  which  thus  traces  a  spiral.  The  radius  vector  re- 
volves around  the  spiral  once  every  twenty-five  years, 
and  the  ratio  between  the  "amount,"  OA',  after  a  com- 
plete revolution,  and  the  original  "principal"  OA,  will  be 
e,  that  is,  2.718,  provided  the  rate  of  interest  is  reckoned 
continuously. 

The  same  spiral  represents  the  accumulation  of  capital, 
whatever  may  be  the  rate  of  interest.  For  a  complete  revolution 
does  not  represent  a  definite  length  of  time,  but  the  purchase 
period  ;  and  it  is  clear  that  a  more  rapid  rate  of  interest  is  repre- 
sented by  a  more  rapid  turning  of  the  radius  vector.  Thus,  if 
the  rate  is  not  4%,  but  8%,  the  radius  vector  swings  around 
through  the  same  spiral  once  in  twelve  and  a  half  years  instead 
of  once  in  twenty -five  years.  Again,  if  the  rate  is  2%,  the 
revolution  is  fifty  years.  The  spiral  is  what  is  known  as  the 
"equiangular  spiral,"  and  has  the  property  that  the  tangent  at 
any  point  is  inclined  at  a  constant  angle  to  the  radius  vector. 

The  angle  is  in  this  case  such  that  its  tangent  is  2?r.     This 

e_ 

angle   is  80°  57'.     The  equation  of  this  spiral  is  —  =  <?"",  in 

"u 

which  p  represents  the  radius  vector,  0  the  angle  of  revolution, 
and  p0  the  initial  radius  vector;  e  and  ?r  are,  of  course,  the 
magnitudes  ordinarily  represented  by  these  letters,  namely,  the 
base  of  the  Napierian  system  of  logarithms  and  the  ratio  of 
the  circumference  of  a  circle  to  its  diameter. 


396  NATURE   OF   CAPITAL   AND    INCOME 


§  1  (TO  CH.  XIV,  §  5) 

When  the  Interest  Rate  varies,  there  are  Two  Rival  Concepts  of  Standard 

Income. 

When  the  rate  of  interest  varies  during  successive  years,  the 
standard  of  the  comparison  of  income  and  capital  requires  re- 
statement. We  found,  when  the  rate  of  interest  was  assumed 
constant,  that  the  standard  income  corresponding  to  a  given 
capital  was  a  perpetual  and  uniform  flow,  of  which  flow  that 
capital  was  at  any  time  the  present  value.  It  did  not  matter 
whether  standard  income  was  conceived  as  income  which 
was  constant  and  perpetual,  or  as  income  which  would  main- 
tain its  capital-value  at  a  constant  level ;  for  under  the  con- 
dition of  a  constant  rate  of  interest,  a  constant  income  will 
necessarily  maintain  a  constant  capital-value.  But  when  we 
introduce  the  possibility  of  a  change  in  the  rate  of  interest, 
these  two  concepts  of  standard  income  are  no  longer  equiva- 
lent; under  such  conditions  only  an  inconstant  income  will 
maintain  a  constant  capital-value.  Thus,  if  the  rate  of  interest 
for  the  first  year  is  10%,  for  the  second,  5%,  and  for  the  third, 
6%,  etc.,  the  income  stream  which  will  maintain  the  capital 
unimpaired  will  be,  in  successive  years,  proportional  to  the 
numbers  10,  5,  6,  etc.  A  person  possessed  of  $100  of  capital 
can  evidently  earn  with  it  $10  the  first  year  and  still  have  his 
.$100  unimpaired,  with  which,  in  turn,  he  can  earn  $5  the 
second  year  and  maintain  the  principal  of  $100 ;  and  again 
$6  in  the  third  year,  and  so  on,  receiving  each  year  an  income 
proportional  to  the  rate  of  interest.  Relatively  to  this  income 
stream  considered  as  a  standard  of  reference,  the  propositions 
stated  in  Chapter  XIII  will  remain  true,  namely,  that  if  the 
real  income  in  any  year  exceeds  the  standard  for  that  year,  the 
capital  will  be  impaired  by  the  excess ;  and  if  the  income  falls 
short  of  the  standard  in  any  year,  the  capital  will  accumulate 
by  the  amount  of  the  deficiency. 

But  this  concept  of  standard  income  is  not  the  only  legiti- 
mate one.  We  may,  if  we  choose,  employ  the  other  definition 
of  standard  income,  as  a  perpetual  and  uniform  flow.  In  this 


AI'l'KNDIX    TO    CHAl'TKR    XIV  397 

case,  it  is  the  capital-value  of  such  an  income  stream  which 
will  vary  from  time  to  time.  As  has  been  seen,  the  capital- 
value  of  such  an  income  stream  is  found  by  dividing  the  rate  of 
income  a  by  the  average  of  the  individual  rates  of  interest,  such 
as,  in  the  above  example,  10%,  5%,  6%,  etc.,  ad  inf.,  the  aver- 
age being  obtained  by  the  formula  given  in  Appendix  to  Chap. 
XII,  §  5.  If  such  average  rate  of  interest  be  called  j1}  the 

capital-value  will  be  -.     Suppose,  for  instance,  that  the  person 

Ji 

has  a  uniform  perpetual  income  of  $5  per  annum.  If  the  rate 
of  interest  to-day,  jlt  is  5%,  the  capital-value  to-day  will  be  $100. 
If  next  year,  j2  (the  average  of  the  future  rates  in  individual 
years,  beginning  at  that  time)  is  4.9%,  the  capital-value  will 
be  $102.  If,  two  years  from  date,  ja  be  5.1%,  the  capital- value 
will  sink  to  $98.  Adopting  such  an  income  stream  as  a  stand- 
ard, the  propositions  as  to  impairment  or  increase  will  still  be 
true,  provided  such  impairment  or  increase  is  measured  with 
reference  to  the  variable  capital-value  just  shown.  Thus,  if  at 
the  end  of  the  first  year  more  income  than  $5  is  received,  the 
capital-value  will  be  impaired  by  the  difference,  this  impair- 
ment to  be  reckoned  with  respect,  not  to  $100,  but  to  $102, 
which  would  be  the  value  had  the  income  remained  standard. 
Thus,  the  effect  of  a  difference  between  real  and  stand- 
ard income  may  be  stated  in  the  same  terms,  whichever  of  the 
two  definitions  of  standard  income  is  adopted.  In  the  one  case 
the  standard  is  with  reference  to  constant  capital  and  variable 
income ;  in  the  other,  to  variable  capital  and  constant  income. 
In  practical  life,  the  former  standard  is  usually  employed, 
although  for  certain  purposes  the  latter  would  be  more  suitable. 
We  all  know  of  cases  of  investors  who,  twenty  years  ago,  in- 
vested at  a  high  rate  of  interest,  and  who  have  taken  pains 
merely  to  maintain  the  value  of  their  capital  unimpaired, 
although  they  were  well  aware  that  the  rate  of  interest  was 
constantly  sinking.  In.  consequence,  these  persons  are  now 
forced,  when  reinvesting,  to  suffer  a  large  decrease  in  income, 
which  could  have  been  avoided  had  they  kept  in  view  the  main- 
tenance, not  of  their  capital,  but  of  their  income,  and  laid  aside 
each  year  a  certain  sum  in  order  to  offset  the  fall  in  the  rate  of 
interest.  The  reason  such  a  procedure  is  not  common  is 


398  NATURE    OF    CAPITAL   AND    INCOME 

that  the  fall  or  other  change  in  the  rate  of  interest  can  never 
be  foreseen  with  precision,  and  thus  a  perfectly  uniform  flow  of 
income  secured,  whereas  it  is  always  possible,  in  the  case  of 
safe  investments,  to  calculate  what  is  necessary  to  maintain 
the  value  of  the  capital  at  a  uniform  level. 

§  2  (TO  CH.  XIV,  §  12) 
Effect  of  Foreknown  Tax  on  Increase  of  Capital 

Let  us  suppose  that  the  three  brothers  invest  in  their  respec- 
tive annuities  without  realizing  that  a  tax  is  to  be  imposed. 
The  first  brother  has  bought  with  his  $10,000  a  perpetual  annu- 
ity of  $500  a  year;  the  second,  a  perpetual  annuity  of  $1000 
deferred  15  years;  and  the  third,  an  annuity  of  $2000  for  six 
years  only.  After  these  investments  have  been  made,  let  us 
suppose  that  the  tax  of  10%  on  income  is  announced.  If  "in- 
come "  is  interpreted  properly,  i.e.  as  simply  the  annuities, 
the  value  of  each  of  the  three  properties  will  immediately 
shrink  by  $1000,  so  that  any  of  the  three  brothers  could  sell 
his  annuity,  subject  to  the  tax,  for  $9000.  But  if  the  "income 
tax"  is  interpreted  as  a  tax  on  "earnings,"  i.e.  on  income  and 
increase  of  capital,  the  announcement  of  such  a  tax  will  not  only 
reduce  the  values  of  the  three  properties  very  unequally,  as  has 
been  shown,  but  will  have  the  further  effect  of  altering  the  very 
annual  increase  in  the  value  of  the  capital  which  is  subject  to 
taxation.  To  show  the  effect  of  this  "  repercussion,"  let  c  rep- 
resent the  value  of  the  capital  of  the  second  brother  (who  saves) 
at  the  end  of  any  year  during  which  no  (true)  income  is  received. 
Thus  c  is  $18,000  at  the  end  of  the  fifteenth  year  when  the  an- 
nuity of  $1000  a  year  is  purchased  ;  for  the  capitalization  of 
the  perpetuity  of  $1000  which  begins  at  that  time  is  $20,000, 
from  which  $2000  is  deducted  as  the  capitalized  tax.  Let  i 
represent  the  rate  of  interest  (as  5%)  and  t  the  tax  rate  (as 
10%).  We  wish  first  to  find  a;,  the  capital-value  one  year 
earlier  than  c.  It  is  clear  that  x  is  the  discounted  value 

of  c  (i.e.  -     —  ]  less  the  discounted  value  of  the  tax,  which 

V      1  +  V 

we  will  suppose  is  due  at  the  end  of   the   year.      The    tax 
is  laid  on  the  increase  of  capital-value    in   the   year,  i.e.  on 


APPENDIX    TO    CHAPTER    XIV 


399 


c  —  x.  As  the  rate  is  t,  the  tax  is  (c  —  x)t.  The  discounted  value 
of  this  tax  is  >— — 1-;-.  This  deducted  from  the  discounted 
value,  -  — ,  of  next  year's  capital-value  is  this  year's  capital- 

r        (c-yV- 

/^  ^— 


1-M 
value,  x ;  /.<?.,  — 


Solving  for  x,  we  have,     a-=  -•         — . 

1  —  t  +  i 

The  tax  itself  is  t(c  —  x),  which,  if  we  substitute  for  x  its  value 

lust  found,  reduces  to  - 

1-t  +  i 

If  we  substitute  for  i  and  t  their  assumed  values,  .05  and  .10, 
we  have  x  =  c  x  .947 

and  tax  —  ex  .0053. 

Substituting  for  c  its  value  at  the  end  of  the  fifteenth  year, 
namely,  $18,000,  we  find  that  x,  the  value  one  year  earlier, 
will  be  18,000  x  .957,  or  $17,046,  and  that  the  value  one  year 
previous  will  be  the  latter  sum  multiplied  likewise  by  .947,  or 
$16,142.56,  and  so  on  until  the  present  is  reached,  when  the 
value  will  be  $7,952.15.  The  table  below  will  show,  there- 
fore, the  total  ei't'ect  of  a  10%  tax  on  the  increase  of  value, 


CAPITAL-VALVE 

INCREASK  or  GAPITAL- 

VAI.FE 

10%  TAX  TJIKIJIX.N 

Beginning 

8  7.952.15 

End  of    1  year 

8,397.20 

§445.05 

$44.51 

End  of    '2  years 

8,867.27 

470.07 

47.01 

End  of    3  years 

9.363.54 

496.27 

49.63 

End  of    4  years 

9,887.58 

524.04 

52.40 

Knd  of    5  years 

10.440.95 

553.37 

55.34 

End  of    0  years 

11,025.29 

584.34 

58.43 

End  of    7  years 

11,042.33 

017.04 

01.70 

End  of    8  years 

12.293.91 

651.58 

65.10 

Knd  of    9  years 

12,982.00 

088.15 

68.82 

Knd  of  10  years 

13.708.02 

720.56 

72.06 

End  of  11  years 

14,475.84 

707.  -22 

76.72 

End  of  \'2  years 

15.2SC.OO 

810.10 

81.02 

End  of  13  years 

10,142.50 

850.50 

85.66 

End  of  14  years 

17.04(3.00 

903.44 

90.34 

Knd  of  15  years 

18.000.00 

954.00 

95.40 

400  NATURE    OF    CAPITAL    AND    INCOME 

including  the   "  repercussion  "   of  the  tax  on  the  capital-values 
themselves. 

The  taxes  in  the  table  evidently  differ  somewhat  from  the 
taxes  given  in  the  text,  which  do  not  include  the  effect  of 
"repercussion."  The  present  value,  therefore,  of  this  tax  on 
the  increase  of  capital  should  be  altered  from  $714  to  $661.81. 
A  similar  correction  should  be  made  for  the  case  of  the  spend- 
thrift. Our  main  object,  however,  is  not  to  study  the  effects 
of  different  methods  of  levying  taxes,  but  merely  to  show  how 
untenable  is  the  theory  which  includes  savings  under  income, 
and  excludes  that  part  of  true  income  or  services  which  brings 
about  a  depreciation  of  capital. 

§  3  (TO  CH.  XIV,  §  13) 
Unrestricted  Application  of  a  True  Income  Tax  Impracticable 

Theoretically,  an  income  tax  should  tax  every  element  of 
income,  large  or  small,  positive  or  negative.  That  is,  all  posi- 
tive items  should  have  a  tax  and  all  negative  items  a  bounty. 
This  system  would  be  ideal  in  theory  but  difficult  to  carry  out 
in  practice. 

No  attempt  is  made  in  this  book  to  contrive  a  practical 
system  of  taxation  which  would  avoid  all  the  difficulties  which 
have  been  pointed  out  as  belonging  to  systems  now  in  use.  It 
is  undoubtedly  true  that  it  would  be  impracticable  to  assess 
taxes  on  each  article  on  the  basis  of  the  actual  items  of  in- 
come it  yields  ;  for  most  of  such  items  are  simply  the  positive 
sides  of  "  interactions"  and  are  offset  as  outgoes  in  the  accounts 
of  some  other  article  of  capital.  To  carry  out  such  a  system  in 
detail  would  require  that  we  levy  taxes  on  the  proceeds  of  every 
sale  and  remit  them  on  every  investment.  It  would  be  difficult 
to  avoid  injustice,  evasion,  and  fraud  if  the  attempt  were  made 
to  assess  taxes  on  such  income  and  remit,  as  Avould  be  required 
logically,  taxes  on  the  corresponding  outgo.  The  taxpayer  would 
contrive  to  exaggerate  his  outgo  and  understate  his  income. 
Consequently,  the  system  is  not  wholly  unjust  which  ex- 
empts from  taxation  that  part  of  income  which  stands 
for  impairment  of  capital,  and  assesses  taxes  on  that  part 
which  swells  capital,  or  savings.  The  system  would  be 


APPENDIX    TO    CHAPTKK    XIV 


401 


entirely  just  if  the  impairment  of  one  capital  were  always 
offset  by  the  equal  increase  of  some  other  capital,  i.e.  if 
the  taxpayer's  total  capital-value  were  kept  at  the  same  level. 
In  general,  large  receipts  are  usually  reinvested  and  should 
therefore  not  be  subject  to  the  income  tax  at  all.  If  we  could 
assume  such  reinvestment  to  be  the  invariable  rule,  we  could 
approve  of  the  system  by  which,  in  England,  a  terminable  an- 
nuity is  not  taxed  as  income  at  its  full  value,  but  is  taxed  only 
on  that  part  of  it  which  constitutes  "interest."  The  other  part, 
which  constitutes  impairment  of  principal,  is  not  taxed.  The 
system,  of  course,  fails  of  justice  in  cases  where  this  impairment 
of  principal  is  never  restored  in  some  other  form  of  investment 
but  ultimately  represents,  like  the  other  part  of  the  annuity, 
through  personal  expenditure,  final  enjoyable  income. 

To  illustrate  the  English  exemption  of  impairment  of  capital, 
if  $1000  is  paid  for  a  five-year  annuity  on  a  basis  of  4  %  inter- 
est (reckoned  semi-annually),  it  will  purchase  an  annuity  of 
$111.33  at  the  end  of  each  six  months,  and  the  following  will 
be  the  schedule  showing  the  capital-value  at  each  interval,  the 
interest  accruing  upon  it,  the  payment  to  the  beneficiary,  and 
the  impairment  of  capital  resulting.1 


CAPITAL 
AT  BEGIN- 
NING 

INTEREST 
ACCRUED 
AT  END 

TOTAL 
PAYMENTS 
AT  KND 

IMPAIR- 
MENT OF 
CAPITAL 

CAPITAL 
LEFT  AT 
END 

1st  half  year    .... 

81000.00  $20.00 

6111.33 

$91.33 

$908.67 

2d  half  year     .... 

908.07     18.17 

111.33 

93.15 

815.52 

3d  half  year     .... 

815.52     16.31 

111.33 

95.02 

720.50 

4th  half  year  .... 

720.50 

14.41 

111.33 

96.92 

623.59 

5th  half  year  .... 

623.59 

12.47 

111.33 

98.86 

524.73 

6th  half  year   .... 

524.73 

10.50 

111.33 

100.83 

423.90 

7th  half  year  .... 

423.90 

8.48 

111.33 

102.85 

321.05 

8th  half  year   .... 

321.05 

6.42 

111.33 

104.91 

216.15 

9th  half  year   .... 

216.15 

4.32 

111.33 

107.00 

109.14 

10th  half  year  .... 

109.14 

2.18 

111.33 

109.14 

000.00 

$1000.00 

If  at  the  start  he  has  a  capital  of  $1000,  at  the  end  of  the 

1  From  Institute  of  Actuaries'  Text-book,  Part  I,  ''Interest,"  by  Ralph 
Todhunter,  p.  57.     Loudou  (Layton),  1901. 

2D 


402  NATURE    OF   CAPITAL   AND   INCOME 

first  half  year,  there  is  left  $ 908. 67,  which  has  impaired 
his  capital  by  $91.33.  This  being  reinvested  and  yielding  in- 
terest, would  make  a  total  combined  fund  of  $1000  as  before. 
At  the  end  of  the  second  half  year,  in  like  manner,  the  original 
security  is  worth  $815.52,  but  to  this  must  be  added  the 
capital  invested  last  year,  $91.33,  and  also  the  investment  this 
year,  $93.15,  making  a  total  again  of  $1000;  and  so  on  for 
each  year. 

If,  then,  as  in  England,  the  tax  is  paid  on  the  interest 
annually  (second  column),  no  injustice  is  done,  providing  the 
items  in  the  fourth  column  are  actually  reinvested  each  year,  and 
that  the  interest  on  such  reinvestment  in  some  other  form  is 
used  as  income.  In  other  words,  each  reinvestment  is  not  ac- 
cumulated at  compound  interest,  but  made  a  separate  fund 
yielding  perpetual  interest  which  is  converted  into  enjoyable 
income  as  fast  as  it  is  received.  In  this  case  the  man  will  be  re- 
ceiving, from  the  given  security  and  the  others  created  out  of 
his  reinvestments,  a  uniform  net  income  of  $20  a  year,  and 
will  maintain  his  capital  at  $1000.  Consequently  the  ex- 
emption of  "impairment  of  capital"  works  no  ultimate  injustice, 
since  ultimately  there  is  no  such  impairment. 

But  as,  practically,  we  can  never  know  to  what  extent  the 
"impairments"  are  actually  reinvested,  the  justification  of  tax- 
ing the  sums  in  the  first  column  instead  of  those  in  the  third 
is  entirely  on  grounds  of  expediency.  Theoretically,  the  actual 
income  from  this  particular  form  of  capital  as  represented  in 
the  third  column  should  be  taxed,  and  afterward  whatever  is 
reinvested  in  some  other  form  should  earn  remission  of  taxes. 
This  method,  while  impracticable  in  such  detailed  application, 
might  with  advantage  be  applied  to  the  taxation  of  an  individ- 
ual's income  as  a  whole.  After  all  the  individual  components 
are  combined  —  all  the  income  elements,  large  or  small,  and  all 
the  outgo  elements,  including  reinvestments  —  there  will  be  a 
resultant  net  income  for  the  individual  which,  and  which  alone, 
should  be  taxed.  A  system  which  would  accomplish  this 
would  tax,  to  this  individual,  any  net  impairment  of  his  capital, 
for  such  impairment  would  mean  large  income;  but,  on  the 
other  hand,  if  he  were  not  depleting  but  laying  up  capital,  it 
would  exempt  the  increase,  for  such  increase  would  not  be  part 


APPKXDIX   TO    CHAPTER    XVI  403 

of  his  income.  Such  a  system  would  secure  justice  in  the  taxa- 
tion of  income.  It  is  practically  what  has  usually  been  called 
the  system  of  taxing  "  consumption." 

APPENDIX    TO    CHAPTER   XVI 

§  1  (TO  On.  XVI,  §  (J) 
Mathematical  Coefficients  of  Probability,  Caution,  and  Risk 

Let  us  call  the  riskless  value  F,  the  mathematical  value  F, 
the  commercial  value  F",  the  coefficient  of  probability  P,  the 
coefficient  of  caution  C,  and  the  entire  coefficient  of  risk  It. 
We  have,  — 

T71  T7""  T^l 

r>  _  ri  _  .  j)  _ 

-F'  F7'  Ii  =  ~V' 

Whence  it  follows  that  R  =  PC. 

That  is,  the  total  effect  of  risk  on  value  is  twofold:  first, 
through  mere  probability,  which  gives  mathematical  value  ;  and 
secondly,  through  caution,  which  gives  commercial  value. 
I*  ractically,  it  is  usually  impossible  to  separate  P  and  C.  The 
object  of  this  analysis  is  not  so  much  to  introduce  the  caution 
factor  explicitly,  as  to  make  the  general  distinction  between  R 
and  P,  and  to  point  out  that  the  actual  market  value  of  secu- 
rities is  not  their  actuarial  or  simple  "  mathematical"  value; 
that,  in  other  words,  R  is  not  the  same  thing  as  P. 

§  2  (TO  CH.  XVI,  §  7) 
Formula  for  Mathematical  Value  of  Risky  Bond 

Let  us  denote  by  r>\  the  probability  of  receiving  the  first 
installment,  a^  of  income  due  in  one  year,  and  by  ^2  the  prob- 
ability of  receiving  the  second  installment  of  income,  «2,  pro- 
vided the  first  years  is  receired,  and  again  by  ps  the  probability 
of  receiving  o3  in  three  years,  prodded  the  preriaus  tiro  hare 
been  received,  and  so  on  for  p4  .  .  .  pH,  where  n  is  the  number  of 
years  to  the  last  payment.  The  chance  of  receiving  the  first 
payment  is  p^;  hence  the  "mathematical  value"  of  the  first 
payment,  when  due.  is  alpl,  the  present  value  of  which  is 

''       But  the  chance  of  receiving  the  second   payment   is 


. 
1-M 


404  NATURE    OF    CAPITAL    AND    INCOME 

evidently  not  p.2,  but  2hlh  5  for  one  of  the  first  principles  of  the 
theory  of  probabilities  is  that  the  chance  of  two  successive  events 
is  the  product  of  their  successive  probabilities.  Thus,  if  the 
chance  of  heads  appearing  in  coin  tossing  is  ^,  the  chance  of  two 
successive  heads  is  i  x  4-,  or  1,  and  the  chance  of  three  succes- 
sive heads  is,  in  like  manner,  1  x  %  X  %,  or  i,  etc.  Hence  the 
"  mathematical  value"  of  the  second  installment,  a2,  when  due  is 

°">PiPto  °f  which  the  present  value  is  a-PlP2.     In  like  manner. 

(!+02 
the  mathematical  present  value   of   the   third   installment   is 

,3.      'I  I  ,  and  so  on.     The  sum  of  the  expressions  for  present 

value  thus  obtained  is  the  total  present  mathematical  value  of 
the  property.  If  we  denote  this  mathematical  value  by  VmJ 
we  have,  — 

'    •  Pn. 


a       ,3l23     ...  | 

i  2     (i  +  O* 

If  we  suppose  that  all  the  probabilities  are  equal,  we  may 
denote  all  the  j/s  simply  by  p,  and  simplify  by  substituting  pz 
for  pipz,  and  p3  for  Pip2p3,  etc. 

Since  the  p's  represent  the  probability  of  receiving  the  in- 
stallments, it  is  clear  that  the  chance  or  risk  of  not  receiving 
them  is  the  difference  between  this  and  unity.  This  risk  of 
default  we  shall  denote  by  the  letter  q.  Thus,  qi=  1  —pi,  etc., 
and  also  p^  =  1  —  q},  etc.  If  all  the  q's  are  equal,  we  shall  de- 
note them  by  g,  and  the  present  value  of  the  property  may  then 
evidently  be  written,  — 

V    =al(1~g)     |.qg(1-?^.l.a3(1-g)3   _|_  I     CTn(l-9)" 

' 


In  case  the  risk  of  default  q  is  very  small,  it  is  evident  that 
the  fraction  —  —  .  is  approximately  equal  to  -  :  -  .    This  may 

be  seen  by  dividing  the  numerator  and  denominator  of  the  first 
fraction  by  1  —  q,  which  will  give  for  the  new  numerator  unity, 

and  for  the  denominator  1  -f-  i  +  q  +  J         {  .    In  this  expression 

1-g 

the  fractional  term  becomes  negligible  when  q  is  small, 
because  the  denominator,  1  —  q,  is  approximately  unity, 
while  the  numerator,  q~  -\-  iq,  is  made  up  of  two  terms,  each  of 


APPKXDIX    TO    CHAPTKU    XVI  405 

which  is  the  product  of  two  very  small  quantities.  Thus,  if  7 
is  T^  and  i  is  T$0-,  the  value  of  the  fractional  term  becomes 
approximately  .0005,  which  is  a  negligible  quantity  (compared 
with  1  +  i  +  q  =  1  4-  .04  4-  .01).  Hence  when  //  is  small,  the 
formula  for  mathematical  value  becomes  approximately,  — 

Y    —  a I ^? | ^3 L.     .  .  .      J an 

W*  T      -4          .  •        i  T  ,  j  ,  >    o        I  /  *  .  .  •  f        I  I  /    4  •  \  «  * 


i  +  q  (l+i  +  qf  (l  +  i  +  qf 
In  other  words,  when  the  risk  of  default  is  small,  its  effect  is 
substantially  the  same  as  that  which  follows  from  a  rise  in  the 
rate  of  interest.  If  the  rate  of  interest  when  risk  is  absent  is 
4%,  a  risk  of  \°J0  will  therefore  merely  increase  the  "basis"  on 
which  the  loan  can  be  contracted  to  about  5%.  Thus,  if  we 
recur  to  the  so-called  5%  ten-year  bond,  and  suppose  that 
the  probability  of  each  successive  payment  is  y9^,  and  the 
risk  of  default,  q,  is  y-J-j,  then  the  mathematical  present  value 
of  the  bond,  when  interest  is  4%,  is  approximately,  — 

F     -  "l  |-  ff2  |  «3  _    ,         etc 

1  +  1  +  3 ^(1  +  i  +  qY  ^(l-M-Hy):i 
^  +  TT-^r,  +  T^T^  + ,  etc. 


1.05  (1.05)2  (1.05)3 
In  other  words,  the  present  value  is  approximately  the  same 
as  the  present  value  of  a  5%  bond  on  a  5%  basis,  which  is  of 
course  par,  or  100. 

But  if  the  risk  is  great,  the  approximate  formula  given  will 
no  longer  apply.  Thus,  if  the  chance  of  default  is  y^,  or,  in 
other  words,  if  the  chance  of  payment  is  only  T!7,  the  formula 
for  the  mathematical  value  of  the  property  becomes,  — 


In  this  case  it  is  evident  that  all  terms  after  the  first  are  neg- 
ligible compared  with  the  first  (unless  the  successive  items  a.,, 
a3,  etc.,  increase  with  sufficient  rapidity  to  offset  the  decreasing 
fractions  y^-,  T^Vij>  etc.).  In  the  case  of  a  5%  ten-year  $100  bond, 
in  which  the  risk  of  default  is  at  any  moment  y9^,  the  approxi- 
mate value  of  the  bond,  obtained  by  omitting  all  terms  after 

5(--} 
the  first,  would  be      v  ^  °  ,  or  approximately  50  cents  !     This 

"  mathematical  value  ''  might  be  still  further  reduced  by  a  co- 
efficient of  caution.  In  other  words,  the  bond  is  worthless.  In 


406  NATURE    OF    CAPITAL   AND    INCOME 

case  of  such  high  risk  we  cannot,  therefore,  apply  the  simple 
rule  of  adding  to  the  rate  of  interest  the  rate  of  risk  to  obtain 
the  "mathematical  value";  and  the  "commercial  value" 
would,  of  course,  be  even  less  than  the  mathematical  value. 
In  other  words,  it  is  practically  impossible  to  compensate  for  a 
risky  investment  by  increasing  the  rate  of  interest  as  though 
it  were  an  insurance  premium.  In  actual  practice  such  a 
"bond"  would  be  absolutely  worthless;  for,  while  the  above 
calculations  are  correct  on  the  basis  of  a  chance  of  payment  of 
one  in  ten,  practically  this  chance  of  payment  would  be  zero. 
The  high  risk  not  only  makes  the  terms  of  the  loan  onerous, 
but  these  onerous  terms  make  the  uncertainty  of  repayment 
greater,  and  so  on  in  a  vicious  circle.  A  lender  who  fancies  he 
can  offset  a  risk  as  high  as  T97  by  lending  only  50  cents  instead  of 
$100  for  a  returnable  principal  of  $100,  will  find  that  he  has 
not  offset  that  risk,  but  merely  increased  it. 

In  the  previous  calculations,  we  assumed  that  a  default  in 
one  payment  carried  with  it  a  default  in  all  subsequent  pay- 
ments. We  may,  however,  easily  extend  our  formula  to  the 
general  case  by  designating  the  chances  of  payment  in  succes- 
sive years,  whether  interdependent  or  not,  by  }h  for  the  first 
year,  p2  for  the  second  (instead  of  by  pl  p2  as  before),  ps  for  the 
third,  etc.,  and  changing  the  first  equation  on  page  404  accord- 
ingly. 


§  3  (TO  Cit.  XVI,  §10) 
Variability  about  a  Mean,  as  measured  by  the  "Standard  Deviation " 

For  a  more  minute  analysis  of  the  bearing  of  chance  it  is 
preferable  to  measure  the  variability  with  reference  to  the 
'iiiean.  Thus,  in  the  case  mentioned,  where  the  dividends  are 
successively  5%,  5%,  C>%,  5%,  5%,  4%,  r>%,  7%,  5%,  3%, 
4%,  5%,  instead  of  measuring  the  variability  of  dividends  with 
reference  to  />%,  we  should  measure  it  with  reference  to  the 
mean  rate,  which  is  4.9%.  The  deviations  from  this  mean 
during  the  twelve  successive  years  were  therefore:  +0.1, 
+  0.1,  +1.1,  +0.1,  +0.1,  -0.9,  +0.1,  +2.1,  +0.1,  -1.9, 
-0.9,  +0.1. 


Al'I'KXDIX    TO    CHAI'TKR    XVI  407 

A  simple  measure  of  the  extent  of  variability  displayed  by 
such  a  series  of  deviations  from  the  mean  is  what  is  called  the 
"  standard  deviation.  "  This  is  a  sort  of  average  of  the  devia- 
tions— not  the  ordinary  arithmetical  mean,  but  the  mean 
found  by  taking  the  arithmetical  mean  of  the  squares  of  the 
deviations  and  extracting  the  square  root.  The  standard 
deviation  which  represents  the  above  twelve  individual  devia- 
tions is  thus,  — 


(.1)2+  (.I)2 4-  (1.1)2+  (.1)-  +  (.1)2+  (-.9)2+  r.l)2  +  (2.1)*  +  M)2 
\  12 

which  is  .95. 

This  "standard  deviation"  is  used  instead  of  other  averages 
for  several  reasons.  The  arithmetical  mean  of  the  deviations 
about  the  mean  is  quite  unavailable,  because,  unless  it  be 
reckoned  by  disregarding  all  minus  signs  (in  which  case  the 
result  is  an  illogical  makeshift),  it  is  zero;  the  standard 
deviation  is  very  readily  calculated,  not  by  performing  the 
operations  indicated  above,  but  by  recourse  to  a  theorem 
that  the  mean  of  the  squares  of  the  deviations  about  the 
mean  is  equal  to  the  mean  of  the  squares  of  the  deviations 
about  any  other  magnitude  less  the  square  of  the  difference 
between  the  mean  and  this  other  magnitude.  The  proof 
of  this  theorem  is  simple,  and  may  be  found  in  the  books 
on  probability.  Applying  it  to  the  illustrated  case,  we  first 
take  the  deviations,  not  about  the  mean,  but  about  some  other 
magnitude,  say  5%.  These  deviations  are  0,  0,  1,  0,  0,  —  1,  0, 
2,  0,  -  2,  -  1,  0.  The  squares  of  these  are  0.  0,  1,  0.  0,  1,  0,  4, 
0,  4,  1,  0,  of  which  the  arithmetical  mean  is  {4,  or  .902.  This 
is  the  mean  of  the  squares  of  the  deviations  about  the  mag- 
nitude 5.  From  this  we  are  to  deduct  the  square  of  the 
difference  between  the  mean  4.9  and  the  other  magnitude  5, 
about  which  the  deviations  were  measured.  The  difference  is 
.1,  its  square  is  .01.  Deducting  this  from  .902  we  have  .892  as 
the  mean  of  the  squares  of  the  deviations  alnnt  the  mean.  The 
square  root  of  this  is  .95,  which  is  therefore  the  standard 
deviation  sought.  Calculated  by  this  method  the  standard 
deviation  may  usually  be  obtained  in  less  than  one  tenth  the 
time  required  by  the  direct  method. 


408  NATURE    OF    CAPITAL   AND    INCOME 

The  "standard  deviation"  plays  an  important  role  in  the 
treatment  of  all  statistics  involving  variation  about  a  mean. 
One  of  its  simplest  uses  is  to  change  any  given  deviation  into 
a  deviation  relative  to  the  standard  deviation  (or  to  a  fixed 
portion  of  it).  This  is  usually  done  by  dividing  the  absolute 
deviation  by  the  standard  deviation.  Thus,  in  the  above  ex- 
ample, where  the  standard  deviation  is  .95  %,  an  absolute  devia- 
tion of,  say,  2  %  mean  is  a  relative  deviation  of  2  ~  .95  or 
about  2.1. 

Such  a  reduction  from  absolute  to  relative  deviation  brings 
the  different  probability  distributions  or  curves  into  a  common 
comparison,  so  that  probability  tables  may  be  constructed 
applicable  to  all.  In  one  case  the  deviations  may  mean  inches 
of  rainfall,  in  another,  pounds  of  barometric  pressure,  in  an- 
other, the  annual  percentage  of  dividends,  as  in  the  case  above. 
These  are  incommeasurable.  But  if  each  be  compared  with 
the  standard  deviation  which  applies  to  that  particular  case, 
and  which  would  therefore  be  measured  in  inches,  pounds,  or 
annual  percentages,  respectively,  we  obtain  three  ratios  which 
are  simply  pure  numbers  indicating  the  extent  of  the  deviation 
compared  with  the  standard  deviation. 

If  we  now  consult  a  probability  table  we  may  find  at  once 
what  is  the  probability  of  any  given  relative  deviation.  For 
the  chance  that  dividends  will,  in  the  case  supposed,  deviate 
in  any  given  future  year  by  2  %  from  the  mean  rate  of  4.9  % 
is,  from  the  tables,  1  in  20 ;  for  the  deviation,  measured 
relatively,  is,  we  saw,  the  number  2.1  and  the  probability  cor- 
responding to  this  in  the  tables1  is  ^.  This  expresses  the 
chance  that  the  deviation  will  keep  inside  the  limits  of  2  %  ; 
i.e.  that  the  dividends  will  be  between  2.9%  and  6.9%. 

The  wider  the  range  of  deviation  considered,  the  less  the 
chance  that  the  actual  dividends  in  any  year  will  fall  out- 
side that  range.  Moreover,  the  chance  decreases  far  faster 
than  the  range  increases.  This  relation,  which  follows  from 
the  theory  of  probability,  has  very  important  consequences  in 

1  Thus  on  p.  55  of  Davenport's  "Statistical  Methods,"  New  York, 
"Wiley.  1809,  we  find  for  a  relative  deviation  2.1,  the  number  .4822  as  the 
chance  of  the  deviation  in  one  direction.  Hence  the  chance  of  the  devia- 
tion in  cither  direction  is  double  this  or  .9044,  about  \'$. 


AITKNDIX    TO    (  HAI'TKR    XVI  409 

the  theory  of  distribution.  From  it  follows  as  a  corollary  that 
the  richer  an  individual,  the  less  risk  in  taking  risks.  Being 
possessed  of  capital,  he  has  a  wider  range  within  which  he  can 
safely  afford  to  operate,  and  therefore  he  has  a  far  greater 
probability  of  keeping  within  these  limits  of  safety  than  his 
less  fortunate  competitors.  Professor  Norton  has  also  empha- 
sized the  fact  that  the  advantage  of  the  capitalist  is  further 
enhanced  by  the  tendency  toward  monopoly.  "  The  result  is  a 
most  interesting  circle,  constant  combination  at  the  top  in 
order  to  force  down  the  commercial  price  of  the  risk,  and 
monopoly  of  the  upper  field,  which  pays  tremendous  prohts, 
resulting  in  still  greater  increase  in  the  financial  power  of  the 
risk  takers.  To  this  there  is  no  end,  save  in  the  divorce, 
through  heredity,  of  ability  and  financial  power.''  J 

An  important  application  of  these  methods  is  to  the  calculation 
of  the  chance  that  earnings  should  fall  below  the  amount  re- 
quired to  pay  interest  on  bonds.  This  chance  is  found  from  the 
probability  table.  It  is  the  probability  corresponding  to  that 
relative  deviation  obtained  by  dividing  the  difference  between 
the  mean  expected  earnings  and  the  interest  by  two  thirds  of 
the  standard  deviation.  In  this  and  other  ways  business  men 
could,  as  Professor  Norton  has  shown,  make  better  use  of  their 
past  experience  than  they  do.  Merely  to  glance  over  past 
earnings  and  receive  an  impression  is  not  a  very  scientific  mode 
of  utilizing  the  facts  which  those  earnings  display.  To  aver- 
age them  is  not  of  much  more  value.  While  it  is  important  to 
know  the  mean,  it  is  also  important  to  know  the  dispersion 
about  the  mean.  This  dispersion  is  shown  by  the  standard 
deviation.  The  best  procedure  would  therefore  seem  to  be  to 
calculate  first  the  mean  of  past  experience  as  to  earnings; 
secondly,  the  standard  deviation  from  that  mean :  thirdly,  the 
chances  of  fluctuations  thus  displayed  (e.g.  the  chance  of 
earnings  falling  below  the  interest-paying  line);  and.  fourthly, 
to  correct  the  results  thus  obtained  by  taking  into  account  the 
degree  in  which  it  is  believed  that  the  future  will  not  follow 
in  the  footsteps  of  the  past.  Only  the  last  of  these  four 
1  From  a  letter  to  the  author.  Cf.  also  Professor  Norton's  '•  Theory  of 
Loan  Credit,"  Publications  of  the  American  Economic  Assuciatwn,  1904, 
p.  54. 


410  NATURE    OF    CAPITAL    AND    INCOME 

operations  need  be  done  by  rule  of  thumb.  But  at  present 
all  but  the  first  and  often  even  that  are  left  to  the  merest  im- 
pression. 

There  was  a  time  when  business  men  did  not  use  bond 
tables,  when  they  did  not  calculate  cost  sheets,  and  even  when 
life  insurance  was  contracted  for  in  scornful  disregard  of  any 
mortality  tables.  Just  as  these  slipshod  methods  have  been 
displaced  by  the  work  of  expert  accountants  and  actuaries,  so 
should  the  mere  guessing  about  future  income  conditions  be 
replaced  by  making  use  of  the  modern  statistical  applications 
of  probability.1 

§  4  (TO  CH.  XVI,  §  20) 
Method  of  computing  a  Pure  Level  Life  Insurance  Premium 

The  chief  peculiarity  of  life  insurance  is  that  each  year's 
premiums,  in  properly  organized  insurance  companies,  are 
calculated  not  on  the  basis  of  the  chance  of  death  in  that 
year,  as  in  the  case  of  fire  insurance,  but  are  computed  as  "  level 
premiums,"  which  exceed  this  chance  in  the  early  years  of 
the  policy,  and  fall  short  of  it  in  later  years.  The  wisdom  of 
such  an  arrangement  is  justified  by  the  incentive  which 
is  produced  for  all  "risks"  to  remain  insured,  whereas  when 
the  "natural"  premium  only  is  charged,  increasing  with 
age,  there  is  a  tendency  for  the  better  risks  to  withdraw, 
making  thereby  a  "selection"  adverse  to  the  companies. 
A  consequence  of  a  "level"  premium  being  charged  is  that 
the  policy  acquires  an  increasing  mathematical  value  with 
time,  so  that  the  policy  holder,  after  a  few  years,  sometimes 
possesses  a  very  valuable  property,  which  he  can,  if  he  chooses, 
sell  or  use  as  collateral  security  for  loans,  etc.  The  value  of 
such  a  policy,  computed  on  the  mathematical  basis,  is  of 

1  Cf.  "The  Put  and  Call,"  by  L.  E.  Higgins,  London,  1902,  pp.  65,  60. 
For  some  suggestions  along  this  line,  see  Kclgeworth,  "  Mathematical 
Theory  of  Banking,"  Jour.  Roy.  Stalls.  Sor.,  March,  1888;  for  a  state- 
ment of  the  modern  statistical  method,  see  Karl  Pearson,  Grammar 
of  Science,  and  his  journal  "Biometrica"  ;  for  an  application  of  this 
method  to  financial  and  industrial  problems,  sec  J.  P.  Norton.  Statis- 
tical Studies  in  the  Nnc  York  Money  Market.  New  Haven  (Tattle.  More- 
house  &  Taylor),  l'J03. 


APPENDIX    TO    CHAPTER    XVI  411 

course  the  present  value  of  the  chance  of  receiving  the  insur- 
ance, less  the  present  value  of  the  chance  of  paying  the 
premiums.  Thus,  for  a  man  aged  .'30,  who  was  insured  10  years 
before,  the  chance  of  his  death  at  the  age  of  35  will  be  about 
-g-fff ff,  or  .86%,  since  of  84,720  living  at  age  30,  about  732  die 
in  their  36th  year.  Hence  the  present  value  of  the  chance  of 
receiving  his  insurance  of  31000  in  that  particular  year  is 
l^tijjjr)  or  $7.07,  assuming  the  rate  of  interest  to  be  4%.  In 
like  manner  we  may  determine  the  present  value  of  the  similar 
chance  for  every  other  year  of  possible  life,  and  the  sum  total 
of  these  present  values  will  be  the  total  present  value  of  the 
chance  of  receiving  the  insurance,  $287.66.  From  this  must  be 
deducted  the  present  value  of  the  chance  that  he  will  pay 
premiums.  Thus,  the  chance  of  his  paying  the  premium  in  the 
above-named  year,  when  he  is  35  years  of  age,  will  be  the 
chance  that  he  will  be  living  at  that  time,  which  is  .958.  This 
multiplied  by  his  premium  and  discounted  gives  the  present 
value  of  this  possible  premium  payment ;  this  added  to  the  like 
sums  for  every  other  year  will  give  the  total  present  value  of 
his  obligation  to  pay  premiums,  $222.86;  this,  in  turn,  sub- 
tracted from  the  present  value  of  the  prospective  insurance 
just  obtained,  namely  $287.66,  will  give  the  present  mathe- 
matical value  of  his  property,  $64.80,  called  the  value  of  his 
insurance,  or  the  "reserve"  on  his  policy. 

The  true  " commercial  value,"  or  the  value  which  he  is  will- 
ing to  pay,  will  be  somewhat  higher.  For,  in  this  case,  the 
coefficient  of  caution  operates  to  increase,  not  to  diminish,  the 
value  of  the  property,  as  insurance  tends,  not  to  make  a  risk, 
but  to  reduce  it. 

The  calculation  of  mathematical  values  of  life  insurance  has 
been  very  perfectly  worked  out.  The  reader  who  is  interested 
will  find  the  most  complete  explanations  in  the  Institute  of 
Actuaries'  Text-book,  2  vols.,  London  (Laytou),  1901. 


INDEX 


Accounting,  philosophical  basis  of, 
129,  140.  Sec  Capital  accounts 
and  Income  accounts. 

Accumulation  of  interest  :  not  in- 
come, but  increase  of  capital, 
134-135,  224;  results  of,  224- 
226. 

Adornment,  services  of,  165. 

Agio  sense  of  rate  of  interest,  195, 
247,  334.  Sec  Premium  con- 
cept. 

Agriculture  amenable  to  prediction, 
291. 

Amortization,  definition  of,  110,  332. 
See  Depreciation  fund. 

Amount  of  a  sum,  definition  of,  203, 
329. 

Amusement,  services  of,  165. 

Annuity,  regarded  as  income,  111; 
concept  of  interest  bused  on 
perpetual,  191-194,  on  termi- 
nable, 194-195;  capital-value  of 
perpetual,  205-208;  "deferred," 
207 ;  examples  of  perpetual, 
208-209;  capital-value  of  ter- 
minable, 209-210;  examples  of 
terminable,  210-211;  the  per- 
petual, taken  as  the  standard 
income,  236-237 ;  sinking  fund 
based  on  difference  between  in- 
come and  ideal  terminable, 
243-244 ;  depreciation  fund 
based  on  difference  between 
actual  income  and  ideal  per- 
petual, 243-244;  mathematical 
formula  for  present  value  of 
perpetual,  369 ;  formula  and 
diagrams  of  capital-value  of, 
payable  annually,  semi-annually, 
etc.,  369-371  ;  formula?  for 
capital-value  of  terminable,  374- 
378 ;  taxation  of  terminable, 
in  England,  401. 

Appraisal  of  labor,    172. 

41 


Appraisal  of  wealth,  methods  used 
in,  11-12,  34-36;  based  on 
future  worth,  204-205. 

Appraised  price,  13 ;  a  source  of 
inaccuracy  in  measurement  of 
wealth,  16-17;  discrepancies 
between,  and  actual  selling  price 
(of  shares  in  stock  company), 
70-72. 

Apprenticeship  considered  as  an 
investment,  169-170. 

Area  method  of  representing  income, 
207-208,  371-374. 

Assets,  definition  of,  67-68,  329; 
discrepancies  in  valuation  of, 
71-72;  effect  of  increase  or 
decrease  in  value  of,  73-74 ; 
fraudulent  methods  of  swelling, 
74 ;  relation  of  stability  of,  to 
capital-balance  necessary  for 
safety  of  a  business,  81  ;  cash, 
quick,  and  slow,  82  ;  true  value 
of  liabilities  derived  from,  84— 
85,  139  ;  items  of,  to  be  included 
in  capital  and  income  accounts, 
139-140  ;  methods  employed  for 
obtaining  valuation  of  bank 
(discount  paper,  short-time 
loans),  194-195,  198-199,  204; 
effect  of  chance  element  on  value 
of,  287-288 ;  figures  of,  of  life 
insurance  companies,  295. 

Assignment,  settlement  of  bank- 
ruptcy by.  86. 

Austria,  taxation  of  forest  lands  in, 
254. 


B 


Balances,  method  of :  in  summing 
capital  or  income  accounts,  90- 
91,  142-143,  183,  335;  taxation 
by,  97-98 ;  contrasted  with 
method  of  couples  in  income 
summation,  157-158. 

Balance  sheet,  definition  of,  329. 


414 


INDEX 


Balance  sheets,  to  show  accumula- 
tion of  surplus,  69 ;  effect  on,  of 
increase  or  decrease  in  value 
of  assets,  73-75 ;  interdepend- 
ence of,  of  different  firms  or 
companies,  87-92 ;  to  show 
methods  of  balances  and  couples, 
91 ;  to  show  distinction  between 
accounting  of  real  and  of  fic- 
titious persons,  93-94 ;  prospects 
of  businesses  shown  by,  264. 

Bank  deposit  rights,  wealth  under- 
lying, 27. 

Bank  notes,  wealth  underlying,  27 ; 
nature  of  property  right  in,  32, 
280;  legal  regulations  govern- 
ing, to  avoid  risk,  289. 

Bank  reserves,  risk-meeting  function 
of,  290. 

Bankruptcies,  communication  of, 
87-88. 

Bankruptcy,  state  of,  82 ;  laws  re- 
lating to,  83;  bondholders'  and 
stockholders'  position  in  case  of, 
83-86  ;  settlement  of,  86 ;  rela- 
tion of  general  crisis  to  indi- 
vidual, 297. 

Banks,  national :  liability  of  stock- 
holders in,  83 ;  investments  of, 
in  government  bonds,  280-281. 

Basis  of  a  security,  definition  of,  329. 

Bemis,  Edward  W.,  cited,  39. 

Bequests  not  counted  as  income,  109. 

Bernoulli's   Theorem,    267,    275. 

Bills   of   exchange,    204-205. 

Bohm-Bawerk,  quoted  on  attempts 
to  define  "capital,"  53-54  ;  con- 
cept of  capital  of,  56 ;  cited, 
60  n.3 ;  statement  that  interest 
is  not  an  element  in  cost  of 
production,  173-174;  cited  in 
connection  with  productivity  | 
theory,  187  ;  concept  of  interest 
of,  195,  247 ;  on  interactions  as 
preparatory  to  enjoyable  serv-  ' 
ices,  318. 

Bondholders,  nature  of  rights  of, 
31-32,  85 ;  distinction  between  i 
stockholders  and,  85,  288-289 ; 
position  of,  in  reorganization 
after  bankruptcy,  85-86 ;  rela- 
tion of,  to  risks  of  enterprises,  289. 

Bonds,  wealth  underlying  property 
in,  25,  26;  nature  of  rights  of 
holder,  31-32,  85;  capital-value 
of,  211-217,  382;  realized  vs.] 


earned  income  of,  231-236; 
application  of  depreciation  fund 
to,  242-243;  as  investments, 
277-281 ;  formulae  for  comput- 
ing value  of,  378-382  ;  formula 
for  mathematical  value  of  risky, 
403-406. 

Bond  value  books,  213-215. 

Bougand,    quoted,    168    n. 

Branford,  Victor,  cited,  63  n. 

Building  and  loan  association,  in- 
come accounts  of,  127-128. 

Bullock,  C.  J.,  definition  of  income 
by,  349-350. 


Call,  option  known  as  a,  298. 

Campbell,  A.  C.,  cited  on  moral 
effects  of  insurance,  295  n. 

Canard,  human  beings  counted  as 
wealth  by,  5  n.2. 

Cannan,  Edwin,  definition  of  wealth 
by,  3 ;  cited  on  definition  of 
capital,  56,  n.1;  cited  in  connec- 
tion with  wage  fund  theory,  59 ; 
use  of  term  "capital"  by,  60 
and  n.7  ;  on  concept  of  income, 
102  n.3;  savings  regarded  as 
income  by,  108 ;  concept  of 
income  of,  116;  on  distinction 
between  rent  and  interest,  186 
n.2;  confusion  of  earned  with 
realized  income  by,  247-248. 

Capital,  concept  of,  as  stock  of  wealth 
at  an  instant  of  time,  51-52, 
324 ;  varying  views  of,  53-57 ; 
relation  of  labor  to,  55 ;  viewed 
as  productive,  56 ;  fancied  dis- 
tinction between  land  and,  56  n.1 ; 
errors  resulting  from  narrow 
interpretations  of,  57-58  ;  rela- 
tion of  author's  definition  to 
established  usage,  60-61 ;  dic- 
tionary definitions  of,  61-62 ; 
business  men's  view  of,  63-65  ; 
two  senses  of,  called  capital- 
goods  and  capital-value,  66-67  ; 
relation  of  surplus  or  undivided 
profits  to,  68-70;  original  and 
net,  69,  330;  bookkeeper's  r.s. 
market's  estimate  of,  70-72 : 
four  separate  meanings  of  term 
applied  to  person  or  firm,  72; 
classification  of,  72:  nominal 
and  paid-up,  72,  330 ;  payment 


INDKX 


41; 


of  dividends  out  of,  7~>,  250; 
of  "real"  person  and  of  "fic- 
titious" person,  92-93;  relation 
of  credit  to,  96  ;  fallacious  sta- 
tistics of,  98 ;  confusion  of  in- 
come and,  105-112,  114-115, 
351  ;  fallacy  of  adding  to  income 
savings  of,  108,  134-135,  247- 
255,  349,  353 ;  income  need  not 
leave  unimpaired,  110-111; 
outgo  is  not,  124;  analogous  to 
and  correlative  with  income, 
184;  physical  productivity  and 
value  productivity  of,  185,  186  ; 
physical  return  and  value  return 
of,  185,  186;  mistake  of  dis- 
tinguishing between  land  and, 
186-187  ;  fundamental  principle 
of  value  of  (value  of  future 
income),  188  ;  increase  of,  equals 
excess  of  earnings  over  income, 
237-238 ;  relation  between 
amount  of,  and  risk  involved, 
277,  408-409;  reserves  of,  held 
to  avoid  risk,  290 ;  representa- 
tion of  income  arid,  by  polar 
coordinates,  393-395;  effect  of 
foreknown  tax  on  increase  of, 
398-400 ;  taxation  of  impair- 
ment of,  400-403. 

Capital  accounts,  definition  of,  67, 
89 ;  methods  of  balances  and 
couples  in  summing  up,  90-92 ; 
relation  between  income  ac- 
counts and,  139,  256-264. 

Capital  balance,  81,  329. 

Capital  cost,  124-125. 

Capital  curves,  303-322,  369-378. 

Capital-goods,  meaning  of  term,  67 
329;  classification  of,  72. 

Capital  instruments,  66-67,  72,  329  ; 
regulation  of  income  by  com- 
bining, 127-129,  245-246. 

Capitalization,  definition  of,  64,  330: 
rate  of,  194;  employment  of 
rate  of,  as  alternative  to  rate 
of  interest,  199  ;  table  showing 
equivalent  rates  of  interest, 
discount,  and,  200 ;  of  income 
by  means  of  rate  of  interest. 202  : 
dimensions  of  rates  of  discount, 
interest,  and,  367-368. 

Capitalize,  use  of  term.  64,  330. 

Capital  property,  67,  72,  330. 

Capital-value,  67,  72,  327,  330  ;  deter- 
mination of,  from  rate  of  inter- 


est, 202;  of  perpetual  annuity, 
205-208,  369;  of  terminable 
annuity,  209-210,  374-378;  risk 
clement  in  determining,  210; 
of  a  bond,  211-217,  382;  of 
any  income  stream,  217-221, 
387-388;  of  alternative  income 
streams,  221-222;  of  group  of 
articles,  223;  is  the  discounted 
value  of  expected  income,  223- 
224,  304-305;  less  than  total 
expected  income,  227-228  ;  effect 
of  change  of  interest  rate  on, 
229,  271-273,  390-393  ;  enumer- 
ation of  causes  affecting,  284- 
285  ;  as  mean  between  past  cost 
and  future  income,  305-309 ; 
formula  for,  of  sum  due  in  one 
year,  and  of  sum  due  at  any  time, 
368. 

Capital-wealth.     See   Capital    goods. 

Carver,  cited,    117  n.2. 

Cash,  income  and  outgo  accounts  of, 
131-132,  135-136;  account  book 
of  lawyer,  136-137;  as  an  in- 
come meter,  137-138. 

Caution,  coefficient  of:  276-277,  330; 
applied  to  insurance,  292  ;  mathe- 
matical presentation  of,  403. 

Census  (U.  S.,  1905),  cited  concern- 
ing railway  valuation,  36  n. 

Certificates,  of  property,  23 ;  ne- 
cessity of  separating  from  wealth, 
property,  services,  and  utility, 
38;  stock,  68-70;  receiver's, 
86. 

Chance,  element  of,  in  property 
rights,  22,  330;  involving  risk 
of  insolvency,  81  ;  nature  of, 
265-269 ;  always  an  estimate, 
266 ;  an  affair  of  ignorance, 
268  ;  measurement  of,  269-271 ; 
mathematical  value  of  a,  275; 
in  valuing  stock,  280-283  :  effect 
of,  on  discount  curve,  286-287  ; 
effect  of,  on  bookkeeping,  287— 
288  ;  effect  of,  on  capital  curves, 
320-322. 

Chen,  Chin  tao,  cited  on  utility,  47. 

Clark,  J.  B.,  cited  on  utility,  47; 
concept  of  capital  of,  55,  56, 
60;  term  "capital-goods"  sug- 
gested by,  67  ;  use  of  economic 
terms  by,  67;  "Niagara  Falls" 
simile  of,  applied  to  income,  129  ; 
distinction  between  work  and 


416 


INDEX 


labor  drawn  by,  175  n. ;  con- 
cept of  interest  of,  247. 

Clothing,  services  of,   165. 

Coefficients  of  caution,  probability, 
and  risk.  See  Caution,  etc. 

Combination  of  capital  instruments 
to  standardize  income,  127-129, 
245-246. 

Commodities,  definition  of,  5,  323, 
331 ;  classification  of,  7  ;  error  of 
reckoning  as  income,  105—106. 

Complete  rights  to  property,  36-37, 
95-96,  324-325,  335. 

Composition,  settlement  of  bank- 
ruptcy by,  86. 

Computation  tables,  243  n.,  283- 
284,  408-411. 

Consumption,  145,  152,  164,  165,  336, 
350. 

Contingent  liability,  83. 

Control,  value  of,  as  applied  to 
railway  ownership,  35-36. 

Copyright,  wealth  underlying,  27, 
29. 

Cost,  included  in  term  "outgo,"  120; 
influence  of  past,  on  present 
value,  188-190. 

Cost  of  production,  151,  173-174, 
184. 

Cotgrave,  definition  of  capital  by, 
62. 

Couple,  definition  of,  331. 

Couples,  method  of :  in  capital  sum- 
mation, 90-91,  183-184,  335; 
applied  to  accounting  of  rail- 
way company,  94 ;  taxation  by, 
97—98 ;  income  summation  bv, 
143-152,  183-184,  335;  natural 
income  discovered  by,  150-151  ; 
contrasted  with  method  of  bal- 
ances in  income  summation,  157- 
158. 

Courcelle-Seneuil,  use  of  term  "capi- 
tal" by,  60. 

Credit,  nature  of  property  right 
represented  by,  32-33;  mis- 
taken view  of,  39;  relation  of, 
to  capital,  96-97;  in  the  sense 
of  an  item  of  a  transaction,  158- 
159,  336. 

"Credited,"  income  said  to  be,  122, 
132,  325. 

Creditors,  regarded  as  risk-takers, 
83-84 ;  bondholders  contrasted 
witli  stockholders  as,  85. 

Crises,  causes  of,  296-2U7. 


Currency    inflation,     mistaken    idea 

the  basis  of,  38-39. 
Custom  (tailor's),  wealth  represented 

by,  29. 

D 

Daniels,  use  of  term  "capital"  by, 
60  n.7. 

Dargun,  human  beings  counted  as 
wealth  by,  5  n.2. 

Davenant,  on  human  beings  as  wealth, 
5  n.2. 

Davenport,  "Statistical  Methods" 
by,  408  n. 

Debit,  an  item  of  a  transaction,  122, 
132,  158-159,  336. 

Debt,  imprisonment  for,  83 ;  repu- 
diation of,  84 ;  payments  on 
(interest  or  principal)  are  outgo, 
134. 

Definition,  tests  of  a,  116. 

De  Foville,  use  of  term  "capital" 
by,  60. 

Depletion  of  capital,  not  to  be  de- 
ducted from  income,  110,  134; 
taxation  and,  400-403. 

Depreciation   not  outgo,   234. 

Depreciation  fund,  regulation  of  in- 
come by,  125-126,  239-243; 
geometrical  figures  representing, 
240,  241. 

Depreciations,  item  of,  in  income  and 
capital  accounts,  257-263. 

Desirability,  concept  of,  41,  326; 
discussion  of  term,  and  term 
"utility,"  42-43.  See  Utility. 

Dimension,   definition  of,   331. 

Dimensions  :  wealth,  price,  and  value, 
3-15,  341-344;  of  income- 
capital  ratios,  186,  357  ;  of  rates 
of  interest,  discount  and  capi- 
talization, 367-368. 

Discommodities,  class  of  articles 
termed,  120. 

Discount,  rate  of,  199,  200,  327,  332; 
table  showing  equivalent  rates 
of  interest,  capitalization,  and, 
200;  total,  on  a  sum,  200-210, 
331  ;  mathematical  relations 
between  rates  of  interest  and, 
364-36(5 ;  between  rates  of, 
for  different  time  reckonings, 
366-367:  dimensions  of  rates 
of  interest,  capitalization,  and, 
307-368. 


INDEX 


417 


Discount  curve  (Exponential  curve), 
203-204,  223-224,  331-332;  ap- 
plications of,  200-208,  272,  284- 
287,  303-309,  317-322,  360-361, 
378,  380-381,  391-394. 

Discount   paper,   banks',   204. 

Disservices,  definition  of,  20,  119- 
120,  325,  332;  enumeration  of, 
120;  measurement  of,  120-121; 
examples  of,  123;  "necessary 
evils,"  123;  one  phase  of,  and 
services  termed  "interactions," 
144  ;  transformations  of  wealth 
from  one  point  of  view  are,  146. 

Distribution  curve  of  incomes,  142. 

Distribution    ledgers,    142,    143. 

Disutility,   criticism  of  term,  42. 

Dividends,  effect  of  payment  of, 
on  capital  account,  75  ;  payment 
of,  out  of  capital,  75,  256 ; 
variability  of,  281-282,  406- 
407. 

"Doses"  of  capital,   185. 

Double  counting,  fallacy  of,  in  con- 
cept of  income,  107-108,  113- 
115,  116,  347,  350;  economists' 
attempts  to  avoid,  109-112. 

Double  entry  bookkeeping,  144,  159, 
325-326. 

Double  taxation,  39,  97-98,  250-253, 
255. 

Du  Gauge,  Dufresne,  definition  of 
capital  by,  02. 


"Earning  power"  of  stock,  71. 

Earnings  (Earned  income),  defini- 
tion of,  234,  333 ;  distinction 
between  realized  income  and, 
234-236,  247-253,  327-328,  353  ; 
excess  of,  over  income,  equals  in- 
crease of  capital,  237-238.  328. 

Edgeworth,  F.  Y.,  definition  of  in- 
come by,  102  ii.1 ;  cited,  410  n. 

Elements  of  income  or  outgo.  121. 

Emery.  H.  C.,  cited  on  speculations, 
300. 

Endorsement,  influence  of,  in  re- 
ducing risk,  2S9. 

Engel.  human  beings  counted  as 
wealth  by,  5  n.-,  17. 

England,  bankruptcy  laws  in,  S3  : 
income  taxation  in.  253.  401. 

Enjoyable  income,  105,  112-113, 
ilS,  325-32G. 

2E 


Enjoyable  objective  services  ("Con- 
sumption"), enumeration  of, 
105. 

Exchange  of  wealth,  10,  11,  22,  149, 
332  ;  analysis  of  an,  158—159. 

Expense,  definition  of,  119-120,  332. 

Exponential  curve.  See  Discount 
curve. 

F 

Factor's  agreement,  property  right 
represented  by,  28. 

Fee  simple,  rights  in,  23 ;  wealth 
underlying,  26 ;  definition  of, 
37  ;  an  asset  having  no  counter- 
part liability  constitutes  a,  95. 

Fetter,  F.  A.,  cited  on  utility,  47; 
definition  of  capital  by,  55  ;  cited 
on  confusion  between  quantity 
and  value  of  wealth,  56  n.1; 
use  of  term  "capital"  by,  60 
11. T  ;  use  of  economic  terms  by, 
67;  concept  of  income  of,  117, 
165,  350-351  ;  on  distinction 
between  rent  and  capital,  186  n.1. 

Fictitious  person,  definition  of,  335; 
accounting  of,  distinguished  from 
that  of  real  person,  92,  138-139, 
153,  160-101. 

Finished  products,  classification  of,  7. 

Flow,   definition   of  a,   332. 

Flow  of  wealth,  income  conceived 
as  a,  51-52,  101  ;  duration  of, 
52;  rate  of,  52,  332. 

Flux,  use  of  term  "capital"  by,  60; 
concept  of  income  of,  117. 

Forecasts,  of  income  from  capital, 
2S3-2S4 ;  by  trade  journals, 
291  ;  speculators  experts  in, 
295  ;  crises  caused  by  a  general 
error  in,  29(5-297. 

Foreclosure,  settlement  of  bank- 
ruptcy by,  SO. 

Forests,  appraisal  of  present  value 
of,  based  on  future  worth,  205; 
taxation  of,  254. 

France,  limited  liability  in.  S3; 
taxation  of  forest  lands  in.  254; 
government  bonds  in.  281. 

Franchise  rights,  wealth  underlying, 
20.  29. 

Franklin  fund,  accumulation  of 
interest  shown  by,  225. 

Fund,  definition  of  a',  332. 

Fund  of  wealth,  capital  conceived 
as  a,  51-52. 


418 


IXDEX 


Future,  value  of  any  capital-good 
dependent  on  the,  188-199,  204- 
205,  223-224;  estimates  of, 
based  on  the  past,  283-284,  291, 
295,  296-297. 

Futures,  trading  in,  298-300. 


G 


Gambling,  uneven  value  of  the 
chances  in,  275 ;  distinction  be- 
tween speculation  and,  295. 

Gaskill,  Alfred,  quoted  on  taxation 
of  forest  lands,  254. 

General  property  tax,  253. 

George,  Henry,  proposition  of,  to 
nationalize  land,  30-31. 

Germany,  appraisal  of  forests  in, 
205  ;  taxation  of  forest  lands  in, 
254. 

Gibbs,  J.  W.,  quoted,  65  n.2. 

Gide,  use  of  economic  terms  by,  43. 

Giffen,  use  of  term  "capital"  by,  60. 

Gold  certificates,  nature  of  property 
right  in,  32. 

Goods :  wealth,  property,  and  serv- 
ices treated  under  term,  41,  327  ; 
not  income,  351. 

Good  will,  wealth  underlying  rights 
of,  27,  28-29. 

Government  bonds,  31-32,  280-281. 

Government  property,  wealth  under- 
lying,  27. 

Government  reports,  reduction  of 
risk  by,  291. 

Government's  taxing  power,  nature 
of,  30. 

"Graveyard   insurance,"  294. 

Gross  income,  definition  of,  121,  333. 

Guaranties,  method  of,  to  avoid 
risk,  288-289. 

Guth,  Franz,  on  income,  356. 

Guyot,  use  of  term  "capital"  by,  60. 


II 


Hadley,  A.  T.,  "  capital  "  according 
to,  60  n.7  ;  concept  of  income  of, 
117;  on  commutation  of  risks, 
289,  299. 

Health  as  wealth,  176. 

Hedging,  shifting  risks  by,  299-300. 

Hermann,  F.  B.  W.  v.,  concept  of 
capital  of,  54,  56 ;  perishable 
goods  regarded  as  non-capital 
by,  63 ;  on  income,  352-353. 


Hicks,  use  of  term  "capital"  by,  61. 

Higgins,  L.  R.,  cited,  410. 

Hire,  rights  of,  wealth  underlying,  26. 

Holland,  T.  E.,  cited  concerning 
definition  of  "rights,"  21. 

Housing  and  warming,  services  of, 
165. 

Human  beings,  considered  as  a  form 
of  wealth,  5,  17  ;  classification  of, 
in  scheme  of  wealth,  7. 

Human  body,  transformation  of 
services  through,  167-168  ;  effect 
of  condition  of,  on  subjective 
and  objective  income,  175-170. 


Ignorance,  element  of,  in  chance,  268  ; 
reduction  of  risk  by  decrease  of, 
291. 

Immaterial  wealth,  items  included 
under,  4 ;  disadvantage  of  the- 
ory of,  39. 

Impairment  of  capital,  110,  134, 
328;  taxation  of,  400-403. 

Imprisonment   for   debt,   83. 

Income,  concept  of,  as  flow  of  serv- 
ices during  period  of  time,  51- 
52,  101,  116-118,  324;  savings 
not  to  be  included  in,  108,  134- 
135,  247-255,  349,  353;  vary- 
ing concepts  of,  101-115,  345- 
356 ;  conceived  as  money-in- 
come, 103-104,  115,  117-118, 
333 ;  obtained  in  kind,  104 ; 
real,  104-106,  112-113;  enjoy- 
able, 105,  112-113,  333;  serv- 
ices only  to  be  regarded  as, 
106-107,  112,  116-118;  fallacy 
of  double  counting  in  concept  of, 
107-108,  113-115,  116,  347, 
350;  not  "regular, "  109  ;  stand- 
ard, 110,  234,  236-237,  328, 
333,  396-398  (see  Standard 
income) ;  need  not  leave  capital 
unimpaired,  110,  328;  needless 
distinctions  between  social  and 
individual,  113-115;  confusion 
of  capital  and,  114-115,  351; 
primary  or  natural,  115,  150, 
333;  social,  116,  141,  333,  348; 
net,  118,  121,  130-131,  333 
(see  Net  income) ;  use  of  term, 
in  two  senses  (services  and  value-), 
121  ;  element  of,  121  ;  gross, 
121,  333  ;  viewed  from  one  point 


1NDKX 


419 


is  outcome  or  yield,  122  n.  ; 
effect  of  depreciation  fund  on, 
125-126,  238-24;*;  other  meth- 
ods of  steadying,  127-120,  243- 
247,  259-203,  293-294;  methods 
of  reckoning  real  person's  (law- 
yer's) and  fictitious  person's 
(railway  corporation's),  130-139 
(see  Income  accounts)  ;  total 
social,  141  ;  distribution  of, 
142-143;  objective,  105;  ob- 
jective and  subjective  final  stage 
of,  1G5-169;  psychic  (subjec- 
tive), 1G7-169,  177, 333;  capital 
analogous  to  and  correlative 
with,  184;  value  of  capital 
derived  from  future,  188 ;  pur- 
chasing power  over,  191  ;  pay- 
able annually  and  semi-annually, 
192;  line  method  of  represent- 
ing, 206-207,  371-372;  area 
method  of  representing,  207- 
208,  371-374;  determining  capi- 
tal-value of,  217-221  ;  case  of 
capital-value  less  than  total  ex- 
pected, 227-228;  realized  vs. 
earned,  231-236,  238,  247-255, 
327-328,  353  ;  perpetual  annuity 
taken  as  the  standard,  236-237 ; 
regulation  of,  by  repair  fund, 
259-263 ;  risk  as  applied  to  im- 
mediate, 275-276 ;  forecasts  of, 
283-284  ;  effect  of  changes  in,  on 
capital-value, 284-285  ;  insurance 
a  means  of  steadying,  293-294 ; 
increase  of  value  is  not,  351  ; 
diagrams  for  continuous  and 
discontinuous,  371-374;  repre- I 
sentation  of  capital  and,  by  ! 
polar  coordinates,  393-395;  two 
rival  concepts  of  standard,  when  i 
interest  rate  varies,  396-398. 
Income  accounts,  services  and  dis- 
services which  enter  into,  119-  ! 
121 ;  for  house  and  lot,  122-126  ;  j 
of  building  and  loan  association, 
127-128 ;  of  lawyer  (real  per- 
son), 131-134,  135-136,  163, 
174-175;  of  railway  corpora- 
tion (fictitious  person).  138- 
139;  relation  between  capital 
accounts  and,  139,  256-264.  325  ; 
items  of  assets  and  liabilities 
to  be  included  in,  139-140. 
325;  of  society  as  a  total,  141- 
142;  of  United  States,  142- 


143;  entrance  of  interactions 
into,  143-145,  325;  of  logging 
camp  and  sawmill,  to  illustrate 
application  of  method  of  couples, 
152-154  ;  of  dry  goods  company, 
to  illustrate  double  entry  book- 
keeping, 159-162;  of  factory 
company,  to  show  relation  be- 
tween capital  accounts  and, 
258-262 ;  summarized  definition 
of,  333. 

Income  and  outgo  accounts,  122- 
140.  See  Income  accounts. 

Income  bonds,  85. 

Income  meter,  "cash"  in  income 
accounts  termed  an,  137-138. 

Income-services,  121. 

Income  summation,  by  method  of 
balances,  90-91,  142-143,  183, 
335 ;  by  method  of  couples, 
143-152^183-184,335;  method 
of  couples  contrasted  with 
method  of  balances  in,  157- 
158. 

Income  tax,  250-253,  398-400;  effect 
on  capital  of  misconceived, 
253-254 ;  unrestricted  applica- 
tion of,  impracticable,  400-403. 

Income-value,  121,  327,333;  rate  of 
interest  a  link  between  capital- 
value  and,  202,  327-328. 

Individual  income,  distinctions  be- 
tween social  and,  113-115. 

Insolvency,  81  ;   true  and  pseudo,  82. 

Installment,  payment  by,  as  a  means 
of  regulating  income,  127,  244— 
245. 

Instrument  of  wealth,  5,  19,  333. 

Insurance,  origins  of,  275-276  ;  avoid- 
ance and  shifting  of  risks  by, 
288,  291-294;  a  means  of 
steadying  income,  293-294 ; 
various  forms  of,  294. 

Insurance  companies,  identity  of 
creditors  and  stockholders  in 
mutual.  85  :  terminable  annuities 
used  by,  210;  bonds  offered  by, 
217;  forecast  of  interest  rate 
by.  274. 

Interactions  between  two  instru- 
ments or  groups  of  instruments, 
144,  325.  334;  formerly  styled 
"productive  services,"  145; 
three  classes  of  (transformation, 
transportation,  and  transfer), 
145-152;  natural  services  of 


420 


INDEX 


capital  consist  of,  152-156; 
shown  by  diagrams  to  be  prepara- 
tory to  enjoyable  services,  317- 
320. 

Interest,  is  capital  and  not  income, 
134-135,  224  ;  not  an  item  in  cost 
of  production,  173-174;  spurious 
distinction  between  rent  and, 
186-187  ;  crude  theories  of,  187- 
188 ;  nominal  principal  and, 
in  case  of  bond,  211-212,  215, 
217  ;  accumulation  of,  224-226  ; 
definition  of  nominal  and  total, 
334. 

Interest,  rate  of:  defined,  191, 
334 ;  various  meanings  of,  ac- 
cording to  frequency  of  pay- 
ment, 192-194,  334;  payable 
annually  and  semi-annually,192 ; 
premium  and  price  concepts 
of,  194-196,  246;  interchange- 
ability  of  premium  and  price 
concepts  of,  196-199;  table 
showing  equivalent  rates  of  dis- 
count, capitalization,  and,  200 ; 
a  link  between  capital- value  and 
income-value,  202,  327;  table 
of,  realized  per  annum  on  three, 
four,  and  five  per  cent  bonds,  214- 
215 ;  effect  on  capital-value  of 
change  in,  229,  271-273,  390- 
393  ;  value-return  may  be  greater 
or  less  than,  229-234;  risk  as 
applied  to,  271-274  ;  forecast  of, 
by  insurance  companies,  274 ; 
riskless,  mathematical,  and  com- 
mercial, 279-280 ;  on  govern- 
ment bonds,  280-281 ;  mathemat- 
ical relations  between  annual, 
semi-annual,  and  quarterly  rates 
conceived  in  price  sense,  357- 
358,  in  premium  sense,  358- 
362  ;  mathematical  relation  be- 
tween, and  rate  of  discount, 
364—366 ;  dimensions  of,  and 
rates  of  discount  and  capitaliza- 
tion, 367-368;  variation  of, 
produces  two  rival  concepts  of 
standard  income,  396-398. 

Interstate  Commerce  Commission, 
Report  of,  cited,  39. 

Inventory,  distinction  between  quan- 
tity, price,  and  value  of  wealth 
shown  in  an,  14. 

Investments,  classification  of,  as 
safe  and  unsafe,  277 ;  relation 


between  amount  of  capital  and 

risk  of,  277,  408-409. 
Irredeemable    paper   money,    wealth 

underlying,   27 ;    nature   of,   30. 
Item  of  wealth,  5,  337. 


James,  William,  quoted,  168  n. 

Jevons,  W.  S.,  use  of  phrase  "final 
utility"  by,  46;  concept  of 
capital  of,  54,  57 ;  use  of  term 
"discommodities"  by,  120; 
cited  on  rent  entering  into  cost 
of  production,  173. 

Joint  stock  companies,  capital  ac- 
counts of,  68-70;  limited  lia- 
bility in,  82-83 ;  shares  in,  as 
example  of  perpetual  annuities, 
209. 

Joint  stock  rights,  wealth  underlving, 
26. 

Juglar,  cited  on  crises,  296. 

K 

Kind,  income  obtained  in,   104. 
Kleinwiichter,  concept  of  capital  of, 

54 ;    raw   materials   regarded    as 

non-capital  bv,  63 ;   011  income, 

102,   351-355." 

Knies,  on  capital,  54,  57,  60. 
Knowledge,     reduction    of     risk    by 

method  of  increasing,  288,  291  ; 

utility  of  speculation  based  on, 

298. 
Komorzynski,  on  capital,  65  n.2. 


Labor,  economists'  views  of  relation 
between  capital  and,  55 ;  de- 
fined as  outgo  in  form  of  human 
exertion.  120,  334 :  as  form  of 
disservice,  145 ;  appraisal  of, 
172;  in  a  sense  the  only  true 
cost  of  production,  175;  dis- 
tinction drawn  between  work 
and,  175  n. 

Labor  power,  316—317. 

Lafrentz,  L.  W.,  use  of  term  "capi- 
tal" by,  63. 

Land,  regarded  as  one  class  of  wealth. 
5,  334  ;  classification  of,  7 ; 
nationalization  of,  30-31,  254; 
fancied  distinction  between  capi- 
tal and,  50  u1. ;  view  of,  as  11011- 


I.VDKX 


capital  by  classical  economists, 
63;  mistake  of  distinguishing 
between  capital  and,  180-187; 
an  example  of  capital  yielding 
ail  approximately  perpetual 
annuity,  209 ;  determination  of 
uses  of,  221  ;  benefits  of  specu- 
lation in,  222  ;  taxation  of,  254. 

Land  improvements,   5,   7,   334. 

Landry,  time  element  in  concept  of 
capital  of,  57. 

Lawyer,  income  and  outgo  accounts 
of,  131-137,  162-164,  174-175. 

Lease,  wealth  underlying  rights  of, 
26,  34-35. 

Liabilities,  definition  of,  67,  325,  334  ; 
relation  of  capital-balance  to, 
looking  to  safety  of  a  business, 
81 ;  true  value  of,  derived  from 
assets,  84-85,  139  ;  consideration 
of,  in  income  and  outgo  accounts, 
134-135,  139-140,  162-164. 

Liability,  limited  and  contingent, 
82-83. 

Life  insurance,  steadying  of  income 
by,  294,  295;  method  of  com- 
puting pure  level  premium, 
410-411. 

Limited  liability,  in  case  of  joint 
stock  company,  82-83. 

Line  method  of  representing  income, 
206-207,  371-372. 

Liquidation,  resulting  from  bank- 
ruptcy, 86  ;  a  crisis  defined  as  a 
time  of  general  and  forced,  296. 

Loans,  short-time :  interest  in.  case 
of,  194-195,  198-199;  rate  of 
discount  employed  for,  199,  204. 

Logging  camp  accounts,  152-157,318. 

Lowell  Institute,  possibilities  of 
accumulation  shown  by,  225. 


M 


MacCulloch,  on  human  beings  as 
wealth,  5  ii.2;  concept  of  capital 
of,  55 ;  quoted  on  wage  fund 
theory.  59. 

Machines,  offsetting  of  depreciation 
in.  241-242. 

MacLeod,  H.  D.,  definition  of  wealth 
by,  4  ;  concept  of  capital  of.  .35  : 
includes  credit  under  capital;  90. 

Marginal  utility  (desirability),  defi- 
nition of,  46,  331  ;  mathematical 
expression  for,  344-345. 


Marshall,  Alfred,  use  of  economic 
terms  by,  43,  40,  01  ;  treatment 
of  capital  by,  54  ;  on  distinction 
between  capital  and  non-capital, 
57;  on  concept  of  income,  114, 
117,  347-348;  on  avoidance  of 
double  counting  in  concept  of 
income,  114;  on  transformation 
of  wealth,  145. 

Marx,  distinction  between  capital 
and  non-capital  according  to, 
55  ;  on  relation  between  capital 
and  labor,  55 ;  denies  that 
capital  is  productive,  56. 

Measurement  of  psychic  income, 
177. 

Measurement  of  services  and  dis- 
services, 19-20,  120-121. 

Measurement  of  wealth,  by  quan- 
tity, 8-9 ;  by  price,  9-11;  by 
value,  13-14 ;  inaccuracies  in, 
15-17 ;  expressed  mathematic- 
ally, 341-344. 

Methods  of  avoiding  risk.  See 
Risk. 

Methods  of  balances  and  couples. 
See  Balances  and  Couples. 

Methods  of  standardizing  income, 
125-129,  243-247,  259-263, 
293-294. 

Meyer,   R.,  on  income,  355-356. 

Mill,  J.  S.,  distinction  between  capi- 
tal and  non-capital  by,  54 ; 
capital  itself  regarded  as  a 
product  by.  55 ;  quoted  on 
wage  fund  theory,  59. 

Miner's  inch,   193.  208-209. 

Mines,  terminable  income  exemplified 
by,  209.  210. 

Mixter,  editor  of  Rae's  Sociological 
Theory  of  Capital,  65  n.1. 

Money,  uniformity  of  measurement 
by  means  of.  15  :  irredeemable 
paper,  27,  30;  distinction  be- 
tween three  elements  (wealth, 
property,  certificates)  to  which 
term  is  applied,  38. 

Money-income,  concept  of.  103-104, 
115.  1 17-118. 

Money  price.  335. 

Money  value.  337. 

Money-wages  not  real  wages,  104. 

Monopoly,  effect  of  tendency  toward, 
on  risk  element.  4(19. 

Monopoly  franchise,  wealth  under- 
Ivine;  rights  of,  25,  27,  2!'. 


422 


IXDEX 


Mortgage,  use  of,  to  maintain  regu- 
larity of  income,  127,  244-245  ; 
reduction  of  risk  by,  289. 

Murray,  J.  A.  H.,  dictionary  definition 
of  income,  02-63,  345-346. 

Mutual  insurance  companies,  credit- 
ors and  stockholders  identical 
in,  85. 


X 


National  banks,  liability  of  stock- 
holders in,  83 ;  government 
bonds  bought  by,  280-281. 

Natural  income,  118,  150;  ascertain- 
ing, by  method  of  couples,  150- 
151. 

Nau,  Carl  H.,  cited,  39. 

Net  capital,  69,  330. 

Net  income,  118,  121,  130-131,  333; 
example  of,  in  case  of  lawyer, 
136-137,  163,  174-175;  lacking 
in  case  of  fictitious  persons. 
138-139;  of  society,  141-143: 
determining  by  method  of  bal- 
ances and  method  of  couples 
157-158;  of  merchant's  stock, 
223. 

Xet  outgo,  definition  of,  121,  335. 

Xet  product,  social  income  conceived 
as  society's,  113-115. 

Nicholson,  J.  S.,  human  beings 
counted  as  wealth  by,  5  n.2 ; 
use  of  term  "capital"  by,  61  : 
on  credit  as  "revenue  capital,'' 
96. 

Norton,  J.  P.,  on  relation  between 
amount  of  capital  and  risk  in- 
volved, 277,  409 ;  on  use  of 
probability  computations,  283 
n.1,  410  n. 

Notes,   wealth  underlying,  26,  28. 

Nourishment,  services  of,   165. 


0 


Objective  cost  of  production  non- 
existent, 173. 

Objective  income,  16.5-169;  points  of 
divergence  of,  from  subjective 
income,  109-176. 

Ofner,  human  beings  counted  as 
wealth  by,  5  n.2. 

Opliolirnity,  42. 

Options,  stork  exchange  (puts  ar.  \ 
calls;,  208-299. 


Out-come,  income  viewed  from  one 
point  becomes,  112  n. 

Outgo,  definition  of,  119,  326,  335; 
element  of,  121;  net,  121,  335; 
use  of,  in  two  senses  (disservices 
and  value),  121  ;  viewed  from 
one  point  is  ingo,  123  n. ;  not 
capital,  124 ;  offsetting  of,  by 
depreciation  fund,  125-126 ; 
method  of  couples  applied  to, 
151—152;  depreciation  is  not, 
234. 

Overvaluation  of  capital,  79-80. 

Owner-method   of   taxation,    97-98. 

Ownership,  meaning  of,  18 ;  partial 
and  total,  34-36,  95-96,  324- 
325,  335 ;  change  in  forms  of,  in 
reorganization  after  bankruptcy, 
86 ;  credit  a  form  of  divided, 
96-97 ;  proper  determination 
of,  in  taxation  of  property,  97- 
98;  change  of,  149-152,  and  see 
Exchange  and  Transfer. 


Palgrave,  definition  of  capital  by,  62. 

Panama  Canal,  example  of  depend- 
ency of  capital-value  on  future 
services,  188-189. 

Panics,  causes  of,  296-297. 

Pareto,  human  beings  counted  as 
wealth  by,  5  ii.2;  introduction 
of  term  "ophelimity"  by,  42; 
cited  on  utility,  47 ;  use  of 
term  "capital"  by,  60;  dis- 
tribution curve  of  incomes  of,  142. 

Partial  rights  to  property,  34-37,  95- 
96,  335. 

Partnership,  wealth  underlying  rights 
in,  26  ;  liability  of  members  of  a, 
83 ;  income  considered  in  re- 
spect to,  130. 

Patent  rights,  wealth  underlying,  27. 

Payment  by  installment  a  means  of 
regulating  income,  127,244-245. 

Pearson,  Karl,  cited,  410  n. 

Pension,  the  diminishing  capital- 
value  of  a,  238-239. 

Person,  fictitious  and  real,  defined, 
335.  Sec  Fictitious  and  Real 
persons. 

Pettv,  on  human  beings  as  wealth, 
5  n.2,  17. 

Phvsical  productivity  of  capital,  185, 
186. 


INDKX 


Physical  return  of  capital,  185,  ISO. 

Piecework,  terms  used  in  measure- 
ment of,  19-20. 

Pierson,  N.  G.,  definition  of  income 
adopted  by,  102  n.1,  34G. 

Pigou,  cited  on  utility,  47. 

Pitt,  oil  sinking  fund,  243. 

Pocket  cash,  risk-meeting  function 
of,  290. 

Polar  coordinates,   representation  of  j 
capital    and    income    by,    393- 
395. 

Practice  (physician's),  wealth  repre- 
sented by,  29. 

Prediction.     Sec  Forecast. 

Preferred  stock,  85 ;  share  of,  to 
illustrate  riskless  value,  280. 

Premium  concept  of  interest,  194- 
196,  247,  334;  interchange- 
ability  of,  with  price  concept, 
196-199,  362-366;  represented 
mathematically  and  by  diagram, 
358-361. 

Price,  Richard,  financial  theories  of, 
243. 

Price,  definition  of,  11,  335;  various 
usages  of  term  (money,  market, 
and  appraised  or  reasonable) . 
13—14 ;  distinction  between 
quantity,  value,  and,  14-15 ; 
relation  of,  to  past  costs  and 
future  expectations,  189-190; 
rate  of  interest  called,  of  money 
or  capital,  191  ;  money,  defined, 
335 ;  dimensions  of  wealth, 
value,  and,  341-344. 

Price  concept  of  interest,  191-194, 
196,  247,  334 ;  interchange- 
ability  of,  with  premium  concept, 
196-199,  362-366;  mathematical 
relations  between  rates  reckoned 
annually,  semi-annually,  etc., 
according  to,  357-358. 

Primary  (natural)   income,    115. 

Principal,  nominal,  in  case  of  bonds,  ' 
211-212,  215,  217,  335. 

Probability,     a     matter     of     human  j 
estimate,     not     merely     mathe- 
matics, 270-271  ;    coefficient  of. 
276-277,   331,   335,   403;    appli- 1 
cation  of  principles  of.  to  valua- 
tion   of   capital,    277-279,    403- 
406  ;   theory  of,  applied  to  insur- 
ance, 295. 

Probability  computations,  2S3-2S4. 
408-410. 


Production,  problem  of,  in  con- 
cept of  capital,  55-50,  145- 
148  ;  cost  of,  151,  173-174, 
184. 

Productive   processes,    145-148,   335. 

Productive  services,    145. 

Productivity,  physical  and  value, 
185-188,  335" 

Productivity    theory,    187-188. 

Profits,  undivided,  68. 

Promises  of  refraining,  wealth  under- 
lying, 27.  28. 

Property,  definition  of,  18,  325,  335; 
rights  in,  20-22;  wealth  and, 
correlative  terms  and  coexten- 
sive, 22-23,  95-96;  types  of 
chief  forms  of,  26-27 ;  partial 
and  total  rights  to,  34-37,  95- 
96,  335  ;  necessity  of  separating 
from  wealth,  certificates  of 
property,  services,  and  utility, 
38 ;  confusion  of  ideas  regard- 
ing, 38-40 ;  regulation  of  in- 
come by  sale  of,  127,  244- 
245. 

Property  rights,  definition  of,  18,  22, 
324,  335  ;  table  illustrating  exist- 
ence of  wealth  behind,  26-27 ; 
overlying  of,  by  one  another,  31  — 
32 ;  classification  of,  36-37 : 
method  of  determining  income 
from  collection  of,  130.  Set 
Ownership. 

Pseudo-insolvency,  82. 

Psychic  income,  167-169,  333; 
measurement  of,  177. 

Purchase,  definition  of,  11,  335. 

Purchasing  power,  use  of  phrase, 
191. 

Put,  option  known  as  a,  299. 


Q 


Quantity,  measurement  of  wealth  in 
units  of,  8-9 ;  distinction  be- 
tween price,  value,  and,  14-15: 
conceived  as  a  fund  (capital 
or  a  flow  (income),  51-52; 
measurement  of  services  by,  120- 
121  ;  ratio  of,  of  services  to 
quantity  of  capital  yielding  those 
services  (physical  productivity), 
1S5  ;  dimensions  of  price,  value, 
and,  341-344. 

Quarries,  terminable  income  exempli- 
fied by.  209,  210. 


424 


INDEX 


R 


Rae,  John,  use  of  economic  terms 
by,  5,  65. 

Railway  bonds,  source  of  income 
from,  130. 

Railway  capital,  fallacious  statis- 
tics of,  98. 

Railway  control,  value  of,  35-36. 

Railways,  disservices  vs.  services  of, 
120;  income  accounts  of,  138— 
139 ;  real  sum  total  of  income 
of,  151 ;  leases  of,  as  examples 
of  perpetual  annuities,  208  ;  fore- 
casting the  value  of  property  in, 
284. 

Rate  of  capitalization,  194,  330. 
See  Capitalization. 

Rate  of  discount,  199,  200,  327-328, 
332.  See  Discount. 

Rate  of  flow,  52,  332.     See  Flow. 

Rate  of  interest.  See  Interest,  rate 
of. 

Rate  of  value-return,  229-238. 

Ratios,  income-capital,  185-186,  357. 

Raw   materials,    classification    of,    7. 

Ray  Act  relating  to  bankruptcy,  83. 

Real  estate,  regarded  as  one  class  of 
wealth,  5 ;  classification  of,  7  ; 
inaccuracy  in  appraisement  of, 
16-17 ;  speculation  in,  221-222, 
254.  See  Land  and  Land  im- 
provements. 

Real  income,  concept  of,  104-100, 
112-113. 

Realized  income  vs.  earned,  231- 
236,  238,  247-255,  327-328, 
353. 

Real  persons,  accounting  of,  dis- 
tinguished from  that  of  fictitious 
persons,  92-93,  138-139,  162- 
164,  174-175. 

Real  wages,   money-wages  not,    104. 

Recapitalization  of  stock  companies, 
70. 

Receiver,  office  of,  in  reorganization 
after  bankruptcy,  86. 

Rent,  as  example  of  transfer  of 
wealth,  150—151  ;  and  cost  of 
production,  173-174;  spurious 
distinction  between  interest  and, 
186-187. 

Reorganization  resulting  from  bank- 
ruptcy, 86. 

Repair  fund,  regulation  of  income 
by,  259-263. 


Repairs,  item  of,  in  income  and  capi- 
tal accounts,  257-263. 

Report  on  Direct  Taxation  cited,  114. 

Repudiation  of  debts,   84. 

Reserves  of  capital  held  to  avoid 
risk,  290. 

Resources.      See  Assets. 

Return.     See  Value  return. 

Ricardo,  on  relation  between  capital 
and  labor,  55  ;  theory  of  rent  of, 
187. 

Rider,  W.,  definition  of  capital  bv, 
62. 

Right,   definition  of  a,  20. 

Right  to  subscribe,  78. 

Rights  in  common,  wealth  under- 
lying, 27. 

Risk,  element  of,  in  determining 
capital-value,  205,  210;  as 
applied  to  rate  of  interest,  271- 
274 ;  as  applied  to  immediate 
income,  275-276  ;  coefficient  of, 
277,  336 ;  relation  between 
amount  of  capital  and,  277, 
408-409  ;  five  methods  of  avoid- 
ing, 288 ;  avoidance  of,  by 
method  of  guaranties,  288-289, 
of  safeguards,  289-291  ;  safety 
devices  for  meeting,  290 ;  re- 
duction of,  by  increasing  knowl- 
edge, 291  ;  avoidance  and  shift- 
ing of,  by  insurance,  291-294 ; 
shifting  of,  to  speculators,  295- 
298;  shifting  by  hedging,  299- 
300;  effect  of  element  of,  on 
capital  curves,  320-322  ;  mathe- 
matical coefficient  of,  403.  See 
Chance. 

Risk   of   insolvency,    81. 

Roosevelt,   Theodore,    170. 

Roscher,  W.,  human  beings  counted 
as  wealth  by,  5  n.2;  treatment 
of  capital  by,  54  ;  definition  of 
income  by,  346-347. 

Runs  on  banks,   296,  297. 


Safeguards,  method  of,  to  avoid 
risk,  288,  289-291. 

Safety  devices,  risk-meeting  func- 
tion of,  290. 

Sale,  definition  of,   11,  336. 

Satisfaction,  concept  of,  41,  324;  dis- 
tinction between  utility  and, 
43-44,  53. 


INDEX 


425 


Savings,  to  be  counted  as  capital ,  not 
income,  108,  134-135,  247-253, 
254-255,  328,  349,  353. 

Sawmill,  income  account  for,  152— 
155,  157,  318-320. 

Say,  J.  H.,  human  beings  counted 
as  wealth  by,  5  n.2 ;  use  of  term 
"capital"  by,  GO. 

Schiifile,  A.  E.  F.,  treatment  of 
capital  by,  54. 

Schmoller,  Gustav,  on  income,  352- 
353. 

Seager,  H.  R.,  definition  of  income 
by,  349. 

S^ligman,  cited  on  utility,  47 ;  use 
of  term  "capital"  by,  60  n.7. 

"Selling   short,"  298-300. 

Senior,  N.  W.,  quoted  on  definition 
of  capital,  53 ;  capital  itself 
regarded  as  a  product  by,  55 ; 
on  capital  as  a  producer  of 
wealth,  56. 

Services,  definition  of,  19,  324,  336 ; 
measurement  of,  19-20,  120- 
121  ;  complete  and  partial 
rights  to,  30-37  ;  to  be  separated 
from  wealth,  property,  certifi- 
cates of  property,  and  utility, 
38 ;  income  conceived  as  flow 
of,  51-52,  101,  116-118,  324; 
commodities  wrongly  combined 
with,  in  concept  of  income,  105- 
106  ;  necessity  of  avoiding  con- 
fusion of  anything  else  with,  in 
income-concept,  106-107;  in- 
finite variety  of,  119;  one  phase 
of,  and  disservices  termed  "in- 
teractions," 144;  transforma- 
tions of  wealth  as,  146  ;  method 
of  couples  applied  to,  152-156: 
enjoyable  objective  ("consump- 
tion"), 164,  165,  336;  stage  of 
final  objective,  165;  subjective, 
166;  classification  of,  17S-179. 

Short-time  loans,  194-195,  198-199, 
204. 

Simmonds,  P.  L.,  definition  of 
capital  by.  62. 

Single    taxation.    253-254. 

Sinking  fund,   243-244,   333. 

Smart,  William,  use  of  term  "capi- 
tal" by,  (50  n.' ;  definition  of 
income  by,  348-349. 

Smith,  Adam,  on  capital,  53,  54, 
56.  58,  61  ;  on  rent  and  income, 
150. 


Social  income,  the  concept  of,  as  "not 
product"  of  society,  113-115; 
author's  concept  of,  114,  118, 
141,  {333;  distinction  between 
individual  income  and,  115-116. 

Space-units  for  measuring  wealth, 
8-9. 

Speculation,  in  real  estate,  222,  230; 
benefits  and  evils  of,  295-298. 

Speculators,  use  of  land  deferred 
by,  222  ;  position  of,  considered, 
230;  risk-meeting  function  of, 
288,  290,  295;  in  futures,  298- 
300. 

Sprague,  C.  E.,  cited  on  meaning  of 
term  "capital,"  63  n. 

Standard  deviation,  measurement  of 
extent  of  variability  by,  406- 
410. 

Standard  income,  110,  234,  333; 
vs.  realized,  234-236,  247-253, 
327-328,  353. 

Stock,  economic  use  of  term,  51, 
336  ;  chance  element  in  valuing 
(in  commercial  sense),  280-283. 

Stock  companies,  capital  accounts 
of,  68-70;  two  valuations  in, 
70-72. 

Stockholders,  liability  of,  in  joint 
stock  companies  and  in  national 
banks,  82-83;  preferred,  85; 
bondholders  and,  contrasted, 
85,  288-289 ;  position  of,  in 
case  of  bankruptcy,  85-86 ; 
risk-taking  function  of,  288-289. 

Stock  jobbing,  74-77. 

Stock  of  wealth,  concept  of  capital 
as  a,  51-52,  323-324. 

Stocks,  contrasted  with  bonds,  85, 
288-289 ;  effect  of  chance  on, 
276-277. 

Stock-watering.   79-80. 

Stream  of  wealth,  concept  of  income 
as  a,  51-52,  323-324. 

Subjective  income,  definition  of, 
168,  326  ;  points  of  divergence  of, 
from  objective  income,  169- 
176.  Sec  Psychic  income. 

Surplus,   GS,  256-257. 


Taussig,    F.    W..    318;    definition    of 

income  by.   349. 
Taxation:     double,     39,     253.     255; 

methods     of     avoiding     double, 


426 


INDEX 


97-98 ;  owner-method  and 
wealth-method  of,  97-98;  of 
income,  250-254,  398^03;  the- 
ory of  advocates  of  single,  254 ; 
of 'land,  254. 

Taxing  power,  wealth  underlying, 
27;  nature  of  government's, 
30-31. 

Tenant,  rights  of,  34-35. 

Time,  element  of :  in  concept  of 
capital,  51-52,  56-57 ;  in  con- 
sidering interest,  196. 

Todhunter,    Ralph,    cited,    401. 

Total  discount  on  a  sum,  209—210, 
374-378. 

Total  social  wealth,  diagrammatic 
summation  of,  316-317. 

Total  utility  (Total  desirability). 
44,  47,  331. 

Trade  journals,  risk  element  dimin- 
ished by,  291. 

Transaction,  definition  of,   159,  336. 

Transfer  of  wealth,  10-11,  149-152, 
158-159,  325,  336. 

Transformation  of  services  through 
the  human  body,  167-168. 

Transformations  of  wealth,  defini- 
tion of,  145,  325,  336  ;  services  or 
disservices  according  to  point 
of  view,  146 ;  examples  of,  147- 
148. 

Transportation  of  wealth,  148-149, 
325,  336. 

Trust,   property  held  in,   31. 

Turgot,  use  of  term  "capital"  by,  60. 

Tuttle,  definition  of  wealth  by,  4 ; 
distinction  between  capital  and 
non-capital  according  to,  55 ; 
use  of  economic  terms  by,  60,  67. 


U 


Undesirability,  definition  of,  42,  336. 

Undesirable  event,    123. 

Undivided  profits,  68,  256-257. 

Usance  of  wealth,    117,   348. 

Use  of  desirable  events,  "utility" 
to  bo  distinguished  from,  19,  43. 

Usufructs,  wealth  underlying  rights 
in,  26. 

Utility,  concept  of,  19,  41,  42-43; 
to  be  separated  from  wealth, 
property,  certificate  of  property, 
and  services,  38  ;  error  of  belief 
that  wealth  constitutes,  39-40; 
distinction  between  satisfaction 


and,  43-44,  53 ;  total  and  mar- 
ginal, 44,  331  ;  consideration  of 
marginal,  44-46 ;  total,  47 ; 
definition  of  marginal,  expressed 
mathematically,  344-345. 


Valuation  of  railways,  35-36,  151, 
284. 

Valuations  in  stock  companies 
(bookkeeper's  and  market's), 
70-72. 

Value,  definition  of,  13,  336-337; 
various  uses  of  term,  and  of 
term  "price,"  13-14;  distinc- 
tion between  quantity,  price, 
and,  14 ;  of  control  in  case  of 
railways,  35-36 ;  measurement 
of  services  by,  120—121  ;  deriva- 
tion of,  from  future  and  not  from 
past,  188-189;  riskless,  mathe- 
matical, and  commercial,  276- 
277,  280-283;  dimensions  of 
wealth,  price,  and,  341-344 ; 
increase  of,  not  income,  351  ; 
formulae  for,  of  bond,  378-380. 
See  Capital-value. 

Value    productivity    of  capital,    185, 

186,  335. 

I  Value  return  of  capital,  185-186, 
188-191,  202,  336;  rate  of,  229- 
238 ;  may  be  greater  or  less  than 
rate  of  interest,  229-231. 

Variation,  of  income,  and  its  rem- 
edies, 125-129,  243-247,  259- 
263,  293-294;  of  rate  of  inter- 
est, 229,  271-273,  284-280, 
390-393,  396-398  ;  of  dividends, 
281-282,  406-407. 

Venn,  theory  of  chance  of,  266, 

W 

Wage    fund   theory,    59. 

Wages,    money,    are  not    real,    104. 

Wagner,  Adolf,  on  income,  125, 
353-354. 

Walker,    Francis,    187. 

\Valras,  human  beings  counted  as 
wealth  by,  5  n.2;  on  capital, 
54,  55-56,  63. 

Waste,  an  example  of  overbalancing 
of  services  by  disservices,  120. 

Water-rights,  an  example  of  per- 
petual annuity,  193,  208-209. 


INDEX 


427 


Wealth,  definition  of,  in  general 
sense,  3-5,  337;  "immaterial," 
4,  39;  classes  of,  distinguished, 
5 ;  definition  of,  in  restricted 
sense,  5— (i,  337  ;  scheme  showing 
classification  of,  7 ;  measure- 
ment  of,  8-17  (sec  Measure- 
ment of  wealth)  ;  transfer  of, 
10-11,  149-1 52  (see  Exchange); 
appraisement  of,  11-12,  34-30 ; 
distinction  between  quantity, 
price,  and  value  of,  14-15 ; 
sources  of  error  in  measure- 
ment of,  15-17;  meaning  of 
ownership  of,  18 ;  services  of 
instruments  of,  defined,  19; 
rights  to  services  of,  20-22 ; 
and  property  correlative  terms 
and  coextensive,  22-23,  95,  90 ; 
cases  in  illustration  of  the  corre- 
lation of,  and  property,  24-3G ; 
table  illustrating  existence  of, 
behind  property  rights,  26-27 ; 
partial  and  total  ownership  of, 
34-36 ;  necessity  of  separating 
from  property,  certificates  of 
property,  services,  and  utility, 
38 ;  division  of,  into  fund  and 
flow,  i.e.  capital  and  income, 
51-53;  transformation  of,  145- 
148 ;  transportation  of,  148- 


149;    health    as,    170;    appraisal 

of,  based  on  future  worth,  204— 

205;     risk-meeting    function    of 

stocks    of,     290 ;      diagrammatic 

summation  of  total  social,  310— 

317  ;    dimensions  of  price,  value, 

and,   341-344. 

Wealth-method    of    taxation,    97-98. 
Wear  and  tear,  depreciation  due  to, 

210-211. 
Weight-units    for   measuring  wealth, 

8-9. 
Weiss,     human     beings    counted     as 

wealth  by,  5  n.2. 
Whitman,  Walt,  176. 
Wieser,  use  of  phrase  "marginal 

utility  "   by,   46. 
Wine,      determination      of      present 

value  of,  based  on  future  worth, 

205. 
Wittstein,     on     human     beings     as 

wealth,  5  n.2. 
Work,  distinction  between  labor  and, 

175  n.2. 
Work   dues,   wealth   underlying,   25, 

26. 


Years'    purchase,    concept    of,    194, 

209,    362. 
Yield,  income  viewed  as,   122  n. 


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